Pertemuan 4
Virgiawan
2025-03-07
par(mfrow=c(3,1))
library(probs)## Warning: package 'probs' was built under R version 4.3.3##
## Attaching package: 'probs'## The following objects are masked from 'package:base':
##
## intersect, setdiff, unionHampiran Normal Terhadap Geometrik
set.seed(123)
populasi = rgeom(20, 0.1)
n1 = 2
contoh_geo1 = urnsamples(populasi, size = 2, replace = F, ordered = F)
mean_geo1 = matrix(apply(contoh_geo1, 1, mean))
n2 = 5
contoh_geo2 = urnsamples(populasi, size = 5, replace = F, ordered = F)
mean_geo2 = matrix(apply(contoh_geo2, 1, mean))
n3 = 10
contoh_geo3 = urnsamples(populasi, size = 10, replace = F, ordered = F)
mean_geo3 = matrix(apply(contoh_geo3, 1, mean))
hist(mean_geo1,main = paste("Hampiran Normal Terhadap Geometrik (n = 2)"),xlab = "xbar")
hist(mean_geo2,main = paste("Hampiran Normal Terhadap Geometrik (n = 5)"),xlab = "xbar")
hist(mean_geo3,main = paste("Hampiran Normal Terhadap Geometrik (n = 10)"),xlab = "xbar") 
### Hampiran Normal Terhadap Eksponensial
par(mfrow=c(3,1))
library(probs)
set.seed(123)
populasi = rexp(20)
n1 = 2
contoh_exp1 = urnsamples(populasi, size = 2, replace = F, ordered = F)
mean_exp1 = matrix(apply(contoh_exp1, 1, mean))
n2 = 5
contoh_exp2 = urnsamples(populasi, size = 5, replace = F, ordered = F)
mean_exp2 = matrix(apply(contoh_exp2, 1, mean))
n3 = 10
contoh_exp3 = urnsamples(populasi, size = 10, replace = F, ordered = F)
mean_exp3 = matrix(apply(contoh_exp3, 1, mean))
hist(mean_exp1,main = paste("Hampiran Normal Terhadap Eksponensial (n = 2)"),xlab = "xbar")
hist(mean_exp2,main = paste("Hampiran Normal Terhadap Eksponensial (n = 5)"),xlab = "xbar")
hist(mean_exp3,main = paste("Hampiran Normal Terhadap Eksponensial (n = 10)"),xlab = "xbar")
### Hampiran Normal Terhadap Seragam
par(mfrow=c(3,1))
library(probs)
set.seed(123)
populasi = runif(20)
n1 = 2
contoh_unif1 = urnsamples(populasi, size = 2, replace = F, ordered = F)
mean_unif1 = matrix(apply(contoh_unif1, 1, mean))
n2 = 5
contoh_unif2 = urnsamples(populasi, size = 5, replace = F, ordered = F)
mean_unif2 = matrix(apply(contoh_unif2, 1, mean))
n3 = 10
contoh_unif3 = urnsamples(populasi, size = 10, replace = F, ordered = F)
mean_unif3 = matrix(apply(contoh_unif3, 1, mean))
hist(mean_unif1,main = paste("Hampiran Normal Terhadap Seragam (n = 2)"),xlab = "xbar")
hist(mean_unif2,main = paste("Hampiran Normal Terhadap Seragam (n = 5)"),xlab = "xbar")
hist(mean_unif3,main = paste("Hampiran Normal Terhadap Seragam (n = 10)"),xlab = "xbar")
Sebaran Percontohan Sebaran Normal
par(mfrow=c(3,1))
library(probs)
set.seed(1299)
populasi = rnorm(20,5,sqrt(12)) # Membangkitkan bil. acak ~ Normal (miu = 5, sigma2 =12)
n1 = 3
contoh_norm1 = urnsamples(populasi, size = 3, replace = F, ordered = F)
contoh_norm1## X1 X2 X3
## 1 1.2759246 4.9063860 0.9127462
## 2 1.2759246 4.9063860 4.7962633
## 3 1.2759246 4.9063860 -0.4960505
## 4 1.2759246 4.9063860 1.3199713
## 5 1.2759246 4.9063860 9.1003173
## 6 1.2759246 4.9063860 7.8230413
## 7 1.2759246 4.9063860 3.9885906
## 8 1.2759246 4.9063860 -1.2761191
## 9 1.2759246 4.9063860 7.1127273
## 10 1.2759246 4.9063860 1.0256657
## 11 1.2759246 4.9063860 15.8759113
## 12 1.2759246 4.9063860 6.6170191
## 13 1.2759246 4.9063860 5.9357163
## 14 1.2759246 4.9063860 7.1021421
## 15 1.2759246 4.9063860 8.1282322
## 16 1.2759246 4.9063860 6.0001488
## 17 1.2759246 4.9063860 3.6230786
## 18 1.2759246 4.9063860 2.4165908
## 19 1.2759246 0.9127462 4.7962633
## 20 1.2759246 0.9127462 -0.4960505
## 21 1.2759246 0.9127462 1.3199713
## 22 1.2759246 0.9127462 9.1003173
## 23 1.2759246 0.9127462 7.8230413
## 24 1.2759246 0.9127462 3.9885906
## 25 1.2759246 0.9127462 -1.2761191
## 26 1.2759246 0.9127462 7.1127273
## 27 1.2759246 0.9127462 1.0256657
## 28 1.2759246 0.9127462 15.8759113
## 29 1.2759246 0.9127462 6.6170191
## 30 1.2759246 0.9127462 5.9357163
## 31 1.2759246 0.9127462 7.1021421
## 32 1.2759246 0.9127462 8.1282322
## 33 1.2759246 0.9127462 6.0001488
## 34 1.2759246 0.9127462 3.6230786
## 35 1.2759246 0.9127462 2.4165908
## 36 1.2759246 4.7962633 -0.4960505
## 37 1.2759246 4.7962633 1.3199713
## 38 1.2759246 4.7962633 9.1003173
## 39 1.2759246 4.7962633 7.8230413
## 40 1.2759246 4.7962633 3.9885906
## 41 1.2759246 4.7962633 -1.2761191
## 42 1.2759246 4.7962633 7.1127273
## 43 1.2759246 4.7962633 1.0256657
## 44 1.2759246 4.7962633 15.8759113
## 45 1.2759246 4.7962633 6.6170191
## 46 1.2759246 4.7962633 5.9357163
## 47 1.2759246 4.7962633 7.1021421
## 48 1.2759246 4.7962633 8.1282322
## 49 1.2759246 4.7962633 6.0001488
## 50 1.2759246 4.7962633 3.6230786
## 51 1.2759246 4.7962633 2.4165908
## 52 1.2759246 -0.4960505 1.3199713
## 53 1.2759246 -0.4960505 9.1003173
## 54 1.2759246 -0.4960505 7.8230413
## 55 1.2759246 -0.4960505 3.9885906
## 56 1.2759246 -0.4960505 -1.2761191
## 57 1.2759246 -0.4960505 7.1127273
## 58 1.2759246 -0.4960505 1.0256657
## 59 1.2759246 -0.4960505 15.8759113
## 60 1.2759246 -0.4960505 6.6170191
## 61 1.2759246 -0.4960505 5.9357163
## 62 1.2759246 -0.4960505 7.1021421
## 63 1.2759246 -0.4960505 8.1282322
## 64 1.2759246 -0.4960505 6.0001488
## 65 1.2759246 -0.4960505 3.6230786
## 66 1.2759246 -0.4960505 2.4165908
## 67 1.2759246 1.3199713 9.1003173
## 68 1.2759246 1.3199713 7.8230413
## 69 1.2759246 1.3199713 3.9885906
## 70 1.2759246 1.3199713 -1.2761191
## 71 1.2759246 1.3199713 7.1127273
## 72 1.2759246 1.3199713 1.0256657
## 73 1.2759246 1.3199713 15.8759113
## 74 1.2759246 1.3199713 6.6170191
## 75 1.2759246 1.3199713 5.9357163
## 76 1.2759246 1.3199713 7.1021421
## 77 1.2759246 1.3199713 8.1282322
## 78 1.2759246 1.3199713 6.0001488
## 79 1.2759246 1.3199713 3.6230786
## 80 1.2759246 1.3199713 2.4165908
## 81 1.2759246 9.1003173 7.8230413
## 82 1.2759246 9.1003173 3.9885906
## 83 1.2759246 9.1003173 -1.2761191
## 84 1.2759246 9.1003173 7.1127273
## 85 1.2759246 9.1003173 1.0256657
## 86 1.2759246 9.1003173 15.8759113
## 87 1.2759246 9.1003173 6.6170191
## 88 1.2759246 9.1003173 5.9357163
## 89 1.2759246 9.1003173 7.1021421
## 90 1.2759246 9.1003173 8.1282322
## 91 1.2759246 9.1003173 6.0001488
## 92 1.2759246 9.1003173 3.6230786
## 93 1.2759246 9.1003173 2.4165908
## 94 1.2759246 7.8230413 3.9885906
## 95 1.2759246 7.8230413 -1.2761191
## 96 1.2759246 7.8230413 7.1127273
## 97 1.2759246 7.8230413 1.0256657
## 98 1.2759246 7.8230413 15.8759113
## 99 1.2759246 7.8230413 6.6170191
## 100 1.2759246 7.8230413 5.9357163
## 101 1.2759246 7.8230413 7.1021421
## 102 1.2759246 7.8230413 8.1282322
## 103 1.2759246 7.8230413 6.0001488
## 104 1.2759246 7.8230413 3.6230786
## 105 1.2759246 7.8230413 2.4165908
## 106 1.2759246 3.9885906 -1.2761191
## 107 1.2759246 3.9885906 7.1127273
## 108 1.2759246 3.9885906 1.0256657
## 109 1.2759246 3.9885906 15.8759113
## 110 1.2759246 3.9885906 6.6170191
## 111 1.2759246 3.9885906 5.9357163
## 112 1.2759246 3.9885906 7.1021421
## 113 1.2759246 3.9885906 8.1282322
## 114 1.2759246 3.9885906 6.0001488
## 115 1.2759246 3.9885906 3.6230786
## 116 1.2759246 3.9885906 2.4165908
## 117 1.2759246 -1.2761191 7.1127273
## 118 1.2759246 -1.2761191 1.0256657
## 119 1.2759246 -1.2761191 15.8759113
## 120 1.2759246 -1.2761191 6.6170191
## 121 1.2759246 -1.2761191 5.9357163
## 122 1.2759246 -1.2761191 7.1021421
## 123 1.2759246 -1.2761191 8.1282322
## 124 1.2759246 -1.2761191 6.0001488
## 125 1.2759246 -1.2761191 3.6230786
## 126 1.2759246 -1.2761191 2.4165908
## 127 1.2759246 7.1127273 1.0256657
## 128 1.2759246 7.1127273 15.8759113
## 129 1.2759246 7.1127273 6.6170191
## 130 1.2759246 7.1127273 5.9357163
## 131 1.2759246 7.1127273 7.1021421
## 132 1.2759246 7.1127273 8.1282322
## 133 1.2759246 7.1127273 6.0001488
## 134 1.2759246 7.1127273 3.6230786
## 135 1.2759246 7.1127273 2.4165908
## 136 1.2759246 1.0256657 15.8759113
## 137 1.2759246 1.0256657 6.6170191
## 138 1.2759246 1.0256657 5.9357163
## 139 1.2759246 1.0256657 7.1021421
## 140 1.2759246 1.0256657 8.1282322
## 141 1.2759246 1.0256657 6.0001488
## 142 1.2759246 1.0256657 3.6230786
## 143 1.2759246 1.0256657 2.4165908
## 144 1.2759246 15.8759113 6.6170191
## 145 1.2759246 15.8759113 5.9357163
## 146 1.2759246 15.8759113 7.1021421
## 147 1.2759246 15.8759113 8.1282322
## 148 1.2759246 15.8759113 6.0001488
## 149 1.2759246 15.8759113 3.6230786
## 150 1.2759246 15.8759113 2.4165908
## 151 1.2759246 6.6170191 5.9357163
## 152 1.2759246 6.6170191 7.1021421
## 153 1.2759246 6.6170191 8.1282322
## 154 1.2759246 6.6170191 6.0001488
## 155 1.2759246 6.6170191 3.6230786
## 156 1.2759246 6.6170191 2.4165908
## 157 1.2759246 5.9357163 7.1021421
## 158 1.2759246 5.9357163 8.1282322
## 159 1.2759246 5.9357163 6.0001488
## 160 1.2759246 5.9357163 3.6230786
## 161 1.2759246 5.9357163 2.4165908
## 162 1.2759246 7.1021421 8.1282322
## 163 1.2759246 7.1021421 6.0001488
## 164 1.2759246 7.1021421 3.6230786
## 165 1.2759246 7.1021421 2.4165908
## 166 1.2759246 8.1282322 6.0001488
## 167 1.2759246 8.1282322 3.6230786
## 168 1.2759246 8.1282322 2.4165908
## 169 1.2759246 6.0001488 3.6230786
## 170 1.2759246 6.0001488 2.4165908
## 171 1.2759246 3.6230786 2.4165908
## 172 4.9063860 0.9127462 4.7962633
## 173 4.9063860 0.9127462 -0.4960505
## 174 4.9063860 0.9127462 1.3199713
## 175 4.9063860 0.9127462 9.1003173
## 176 4.9063860 0.9127462 7.8230413
## 177 4.9063860 0.9127462 3.9885906
## 178 4.9063860 0.9127462 -1.2761191
## 179 4.9063860 0.9127462 7.1127273
## 180 4.9063860 0.9127462 1.0256657
## 181 4.9063860 0.9127462 15.8759113
## 182 4.9063860 0.9127462 6.6170191
## 183 4.9063860 0.9127462 5.9357163
## 184 4.9063860 0.9127462 7.1021421
## 185 4.9063860 0.9127462 8.1282322
## 186 4.9063860 0.9127462 6.0001488
## 187 4.9063860 0.9127462 3.6230786
## 188 4.9063860 0.9127462 2.4165908
## 189 4.9063860 4.7962633 -0.4960505
## 190 4.9063860 4.7962633 1.3199713
## 191 4.9063860 4.7962633 9.1003173
## 192 4.9063860 4.7962633 7.8230413
## 193 4.9063860 4.7962633 3.9885906
## 194 4.9063860 4.7962633 -1.2761191
## 195 4.9063860 4.7962633 7.1127273
## 196 4.9063860 4.7962633 1.0256657
## 197 4.9063860 4.7962633 15.8759113
## 198 4.9063860 4.7962633 6.6170191
## 199 4.9063860 4.7962633 5.9357163
## 200 4.9063860 4.7962633 7.1021421
## 201 4.9063860 4.7962633 8.1282322
## 202 4.9063860 4.7962633 6.0001488
## 203 4.9063860 4.7962633 3.6230786
## 204 4.9063860 4.7962633 2.4165908
## 205 4.9063860 -0.4960505 1.3199713
## 206 4.9063860 -0.4960505 9.1003173
## 207 4.9063860 -0.4960505 7.8230413
## 208 4.9063860 -0.4960505 3.9885906
## 209 4.9063860 -0.4960505 -1.2761191
## 210 4.9063860 -0.4960505 7.1127273
## 211 4.9063860 -0.4960505 1.0256657
## 212 4.9063860 -0.4960505 15.8759113
## 213 4.9063860 -0.4960505 6.6170191
## 214 4.9063860 -0.4960505 5.9357163
## 215 4.9063860 -0.4960505 7.1021421
## 216 4.9063860 -0.4960505 8.1282322
## 217 4.9063860 -0.4960505 6.0001488
## 218 4.9063860 -0.4960505 3.6230786
## 219 4.9063860 -0.4960505 2.4165908
## 220 4.9063860 1.3199713 9.1003173
## 221 4.9063860 1.3199713 7.8230413
## 222 4.9063860 1.3199713 3.9885906
## 223 4.9063860 1.3199713 -1.2761191
## 224 4.9063860 1.3199713 7.1127273
## 225 4.9063860 1.3199713 1.0256657
## 226 4.9063860 1.3199713 15.8759113
## 227 4.9063860 1.3199713 6.6170191
## 228 4.9063860 1.3199713 5.9357163
## 229 4.9063860 1.3199713 7.1021421
## 230 4.9063860 1.3199713 8.1282322
## 231 4.9063860 1.3199713 6.0001488
## 232 4.9063860 1.3199713 3.6230786
## 233 4.9063860 1.3199713 2.4165908
## 234 4.9063860 9.1003173 7.8230413
## 235 4.9063860 9.1003173 3.9885906
## 236 4.9063860 9.1003173 -1.2761191
## 237 4.9063860 9.1003173 7.1127273
## 238 4.9063860 9.1003173 1.0256657
## 239 4.9063860 9.1003173 15.8759113
## 240 4.9063860 9.1003173 6.6170191
## 241 4.9063860 9.1003173 5.9357163
## 242 4.9063860 9.1003173 7.1021421
## 243 4.9063860 9.1003173 8.1282322
## 244 4.9063860 9.1003173 6.0001488
## 245 4.9063860 9.1003173 3.6230786
## 246 4.9063860 9.1003173 2.4165908
## 247 4.9063860 7.8230413 3.9885906
## 248 4.9063860 7.8230413 -1.2761191
## 249 4.9063860 7.8230413 7.1127273
## 250 4.9063860 7.8230413 1.0256657
## 251 4.9063860 7.8230413 15.8759113
## 252 4.9063860 7.8230413 6.6170191
## 253 4.9063860 7.8230413 5.9357163
## 254 4.9063860 7.8230413 7.1021421
## 255 4.9063860 7.8230413 8.1282322
## 256 4.9063860 7.8230413 6.0001488
## 257 4.9063860 7.8230413 3.6230786
## 258 4.9063860 7.8230413 2.4165908
## 259 4.9063860 3.9885906 -1.2761191
## 260 4.9063860 3.9885906 7.1127273
## 261 4.9063860 3.9885906 1.0256657
## 262 4.9063860 3.9885906 15.8759113
## 263 4.9063860 3.9885906 6.6170191
## 264 4.9063860 3.9885906 5.9357163
## 265 4.9063860 3.9885906 7.1021421
## 266 4.9063860 3.9885906 8.1282322
## 267 4.9063860 3.9885906 6.0001488
## 268 4.9063860 3.9885906 3.6230786
## 269 4.9063860 3.9885906 2.4165908
## 270 4.9063860 -1.2761191 7.1127273
## 271 4.9063860 -1.2761191 1.0256657
## 272 4.9063860 -1.2761191 15.8759113
## 273 4.9063860 -1.2761191 6.6170191
## 274 4.9063860 -1.2761191 5.9357163
## 275 4.9063860 -1.2761191 7.1021421
## 276 4.9063860 -1.2761191 8.1282322
## 277 4.9063860 -1.2761191 6.0001488
## 278 4.9063860 -1.2761191 3.6230786
## 279 4.9063860 -1.2761191 2.4165908
## 280 4.9063860 7.1127273 1.0256657
## 281 4.9063860 7.1127273 15.8759113
## 282 4.9063860 7.1127273 6.6170191
## 283 4.9063860 7.1127273 5.9357163
## 284 4.9063860 7.1127273 7.1021421
## 285 4.9063860 7.1127273 8.1282322
## 286 4.9063860 7.1127273 6.0001488
## 287 4.9063860 7.1127273 3.6230786
## 288 4.9063860 7.1127273 2.4165908
## 289 4.9063860 1.0256657 15.8759113
## 290 4.9063860 1.0256657 6.6170191
## 291 4.9063860 1.0256657 5.9357163
## 292 4.9063860 1.0256657 7.1021421
## 293 4.9063860 1.0256657 8.1282322
## 294 4.9063860 1.0256657 6.0001488
## 295 4.9063860 1.0256657 3.6230786
## 296 4.9063860 1.0256657 2.4165908
## 297 4.9063860 15.8759113 6.6170191
## 298 4.9063860 15.8759113 5.9357163
## 299 4.9063860 15.8759113 7.1021421
## 300 4.9063860 15.8759113 8.1282322
## 301 4.9063860 15.8759113 6.0001488
## 302 4.9063860 15.8759113 3.6230786
## 303 4.9063860 15.8759113 2.4165908
## 304 4.9063860 6.6170191 5.9357163
## 305 4.9063860 6.6170191 7.1021421
## 306 4.9063860 6.6170191 8.1282322
## 307 4.9063860 6.6170191 6.0001488
## 308 4.9063860 6.6170191 3.6230786
## 309 4.9063860 6.6170191 2.4165908
## 310 4.9063860 5.9357163 7.1021421
## 311 4.9063860 5.9357163 8.1282322
## 312 4.9063860 5.9357163 6.0001488
## 313 4.9063860 5.9357163 3.6230786
## 314 4.9063860 5.9357163 2.4165908
## 315 4.9063860 7.1021421 8.1282322
## 316 4.9063860 7.1021421 6.0001488
## 317 4.9063860 7.1021421 3.6230786
## 318 4.9063860 7.1021421 2.4165908
## 319 4.9063860 8.1282322 6.0001488
## 320 4.9063860 8.1282322 3.6230786
## 321 4.9063860 8.1282322 2.4165908
## 322 4.9063860 6.0001488 3.6230786
## 323 4.9063860 6.0001488 2.4165908
## 324 4.9063860 3.6230786 2.4165908
## 325 0.9127462 4.7962633 -0.4960505
## 326 0.9127462 4.7962633 1.3199713
## 327 0.9127462 4.7962633 9.1003173
## 328 0.9127462 4.7962633 7.8230413
## 329 0.9127462 4.7962633 3.9885906
## 330 0.9127462 4.7962633 -1.2761191
## 331 0.9127462 4.7962633 7.1127273
## 332 0.9127462 4.7962633 1.0256657
## 333 0.9127462 4.7962633 15.8759113
## 334 0.9127462 4.7962633 6.6170191
## 335 0.9127462 4.7962633 5.9357163
## 336 0.9127462 4.7962633 7.1021421
## 337 0.9127462 4.7962633 8.1282322
## 338 0.9127462 4.7962633 6.0001488
## 339 0.9127462 4.7962633 3.6230786
## 340 0.9127462 4.7962633 2.4165908
## 341 0.9127462 -0.4960505 1.3199713
## 342 0.9127462 -0.4960505 9.1003173
## 343 0.9127462 -0.4960505 7.8230413
## 344 0.9127462 -0.4960505 3.9885906
## 345 0.9127462 -0.4960505 -1.2761191
## 346 0.9127462 -0.4960505 7.1127273
## 347 0.9127462 -0.4960505 1.0256657
## 348 0.9127462 -0.4960505 15.8759113
## 349 0.9127462 -0.4960505 6.6170191
## 350 0.9127462 -0.4960505 5.9357163
## 351 0.9127462 -0.4960505 7.1021421
## 352 0.9127462 -0.4960505 8.1282322
## 353 0.9127462 -0.4960505 6.0001488
## 354 0.9127462 -0.4960505 3.6230786
## 355 0.9127462 -0.4960505 2.4165908
## 356 0.9127462 1.3199713 9.1003173
## 357 0.9127462 1.3199713 7.8230413
## 358 0.9127462 1.3199713 3.9885906
## 359 0.9127462 1.3199713 -1.2761191
## 360 0.9127462 1.3199713 7.1127273
## 361 0.9127462 1.3199713 1.0256657
## 362 0.9127462 1.3199713 15.8759113
## 363 0.9127462 1.3199713 6.6170191
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## 776 1.3199713 3.6230786 2.4165908
## 777 9.1003173 7.8230413 3.9885906
## 778 9.1003173 7.8230413 -1.2761191
## 779 9.1003173 7.8230413 7.1127273
## 780 9.1003173 7.8230413 1.0256657
## 781 9.1003173 7.8230413 15.8759113
## 782 9.1003173 7.8230413 6.6170191
## 783 9.1003173 7.8230413 5.9357163
## 784 9.1003173 7.8230413 7.1021421
## 785 9.1003173 7.8230413 8.1282322
## 786 9.1003173 7.8230413 6.0001488
## 787 9.1003173 7.8230413 3.6230786
## 788 9.1003173 7.8230413 2.4165908
## 789 9.1003173 3.9885906 -1.2761191
## 790 9.1003173 3.9885906 7.1127273
## 791 9.1003173 3.9885906 1.0256657
## 792 9.1003173 3.9885906 15.8759113
## 793 9.1003173 3.9885906 6.6170191
## 794 9.1003173 3.9885906 5.9357163
## 795 9.1003173 3.9885906 7.1021421
## 796 9.1003173 3.9885906 8.1282322
## 797 9.1003173 3.9885906 6.0001488
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## 800 9.1003173 -1.2761191 7.1127273
## 801 9.1003173 -1.2761191 1.0256657
## 802 9.1003173 -1.2761191 15.8759113
## 803 9.1003173 -1.2761191 6.6170191
## 804 9.1003173 -1.2761191 5.9357163
## 805 9.1003173 -1.2761191 7.1021421
## 806 9.1003173 -1.2761191 8.1282322
## 807 9.1003173 -1.2761191 6.0001488
## 808 9.1003173 -1.2761191 3.6230786
## 809 9.1003173 -1.2761191 2.4165908
## 810 9.1003173 7.1127273 1.0256657
## 811 9.1003173 7.1127273 15.8759113
## 812 9.1003173 7.1127273 6.6170191
## 813 9.1003173 7.1127273 5.9357163
## 814 9.1003173 7.1127273 7.1021421
## 815 9.1003173 7.1127273 8.1282322
## 816 9.1003173 7.1127273 6.0001488
## 817 9.1003173 7.1127273 3.6230786
## 818 9.1003173 7.1127273 2.4165908
## 819 9.1003173 1.0256657 15.8759113
## 820 9.1003173 1.0256657 6.6170191
## 821 9.1003173 1.0256657 5.9357163
## 822 9.1003173 1.0256657 7.1021421
## 823 9.1003173 1.0256657 8.1282322
## 824 9.1003173 1.0256657 6.0001488
## 825 9.1003173 1.0256657 3.6230786
## 826 9.1003173 1.0256657 2.4165908
## 827 9.1003173 15.8759113 6.6170191
## 828 9.1003173 15.8759113 5.9357163
## 829 9.1003173 15.8759113 7.1021421
## 830 9.1003173 15.8759113 8.1282322
## 831 9.1003173 15.8759113 6.0001488
## 832 9.1003173 15.8759113 3.6230786
## 833 9.1003173 15.8759113 2.4165908
## 834 9.1003173 6.6170191 5.9357163
## 835 9.1003173 6.6170191 7.1021421
## 836 9.1003173 6.6170191 8.1282322
## 837 9.1003173 6.6170191 6.0001488
## 838 9.1003173 6.6170191 3.6230786
## 839 9.1003173 6.6170191 2.4165908
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## 841 9.1003173 5.9357163 8.1282322
## 842 9.1003173 5.9357163 6.0001488
## 843 9.1003173 5.9357163 3.6230786
## 844 9.1003173 5.9357163 2.4165908
## 845 9.1003173 7.1021421 8.1282322
## 846 9.1003173 7.1021421 6.0001488
## 847 9.1003173 7.1021421 3.6230786
## 848 9.1003173 7.1021421 2.4165908
## 849 9.1003173 8.1282322 6.0001488
## 850 9.1003173 8.1282322 3.6230786
## 851 9.1003173 8.1282322 2.4165908
## 852 9.1003173 6.0001488 3.6230786
## 853 9.1003173 6.0001488 2.4165908
## 854 9.1003173 3.6230786 2.4165908
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## 856 7.8230413 3.9885906 7.1127273
## 857 7.8230413 3.9885906 1.0256657
## 858 7.8230413 3.9885906 15.8759113
## 859 7.8230413 3.9885906 6.6170191
## 860 7.8230413 3.9885906 5.9357163
## 861 7.8230413 3.9885906 7.1021421
## 862 7.8230413 3.9885906 8.1282322
## 863 7.8230413 3.9885906 6.0001488
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## 865 7.8230413 3.9885906 2.4165908
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## 872 7.8230413 -1.2761191 8.1282322
## 873 7.8230413 -1.2761191 6.0001488
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## 875 7.8230413 -1.2761191 2.4165908
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## 881 7.8230413 7.1127273 8.1282322
## 882 7.8230413 7.1127273 6.0001488
## 883 7.8230413 7.1127273 3.6230786
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## 889 7.8230413 1.0256657 8.1282322
## 890 7.8230413 1.0256657 6.0001488
## 891 7.8230413 1.0256657 3.6230786
## 892 7.8230413 1.0256657 2.4165908
## 893 7.8230413 15.8759113 6.6170191
## 894 7.8230413 15.8759113 5.9357163
## 895 7.8230413 15.8759113 7.1021421
## 896 7.8230413 15.8759113 8.1282322
## 897 7.8230413 15.8759113 6.0001488
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## 910 7.8230413 5.9357163 2.4165908
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## 913 7.8230413 7.1021421 3.6230786
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## 915 7.8230413 8.1282322 6.0001488
## 916 7.8230413 8.1282322 3.6230786
## 917 7.8230413 8.1282322 2.4165908
## 918 7.8230413 6.0001488 3.6230786
## 919 7.8230413 6.0001488 2.4165908
## 920 7.8230413 3.6230786 2.4165908
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## 925 3.9885906 -1.2761191 5.9357163
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## 927 3.9885906 -1.2761191 8.1282322
## 928 3.9885906 -1.2761191 6.0001488
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## 930 3.9885906 -1.2761191 2.4165908
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## 936 3.9885906 7.1127273 8.1282322
## 937 3.9885906 7.1127273 6.0001488
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## 942 3.9885906 1.0256657 5.9357163
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## 944 3.9885906 1.0256657 8.1282322
## 945 3.9885906 1.0256657 6.0001488
## 946 3.9885906 1.0256657 3.6230786
## 947 3.9885906 1.0256657 2.4165908
## 948 3.9885906 15.8759113 6.6170191
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## 951 3.9885906 15.8759113 8.1282322
## 952 3.9885906 15.8759113 6.0001488
## 953 3.9885906 15.8759113 3.6230786
## 954 3.9885906 15.8759113 2.4165908
## 955 3.9885906 6.6170191 5.9357163
## 956 3.9885906 6.6170191 7.1021421
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## 958 3.9885906 6.6170191 6.0001488
## 959 3.9885906 6.6170191 3.6230786
## 960 3.9885906 6.6170191 2.4165908
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## 962 3.9885906 5.9357163 8.1282322
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## 964 3.9885906 5.9357163 3.6230786
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## 966 3.9885906 7.1021421 8.1282322
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## 968 3.9885906 7.1021421 3.6230786
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## 970 3.9885906 8.1282322 6.0001488
## 971 3.9885906 8.1282322 3.6230786
## 972 3.9885906 8.1282322 2.4165908
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## 981 -1.2761191 7.1127273 8.1282322
## 982 -1.2761191 7.1127273 6.0001488
## 983 -1.2761191 7.1127273 3.6230786
## 984 -1.2761191 7.1127273 2.4165908
## 985 -1.2761191 1.0256657 15.8759113
## 986 -1.2761191 1.0256657 6.6170191
## 987 -1.2761191 1.0256657 5.9357163
## 988 -1.2761191 1.0256657 7.1021421
## 989 -1.2761191 1.0256657 8.1282322
## 990 -1.2761191 1.0256657 6.0001488
## 991 -1.2761191 1.0256657 3.6230786
## 992 -1.2761191 1.0256657 2.4165908
## 993 -1.2761191 15.8759113 6.6170191
## 994 -1.2761191 15.8759113 5.9357163
## 995 -1.2761191 15.8759113 7.1021421
## 996 -1.2761191 15.8759113 8.1282322
## 997 -1.2761191 15.8759113 6.0001488
## 998 -1.2761191 15.8759113 3.6230786
## 999 -1.2761191 15.8759113 2.4165908
## 1000 -1.2761191 6.6170191 5.9357163
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## 1004 -1.2761191 6.6170191 3.6230786
## 1005 -1.2761191 6.6170191 2.4165908
## 1006 -1.2761191 5.9357163 7.1021421
## 1007 -1.2761191 5.9357163 8.1282322
## 1008 -1.2761191 5.9357163 6.0001488
## 1009 -1.2761191 5.9357163 3.6230786
## 1010 -1.2761191 5.9357163 2.4165908
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## 1012 -1.2761191 7.1021421 6.0001488
## 1013 -1.2761191 7.1021421 3.6230786
## 1014 -1.2761191 7.1021421 2.4165908
## 1015 -1.2761191 8.1282322 6.0001488
## 1016 -1.2761191 8.1282322 3.6230786
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## 1018 -1.2761191 6.0001488 3.6230786
## 1019 -1.2761191 6.0001488 2.4165908
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## 1026 7.1127273 1.0256657 6.0001488
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## 1028 7.1127273 1.0256657 2.4165908
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## 1030 7.1127273 15.8759113 5.9357163
## 1031 7.1127273 15.8759113 7.1021421
## 1032 7.1127273 15.8759113 8.1282322
## 1033 7.1127273 15.8759113 6.0001488
## 1034 7.1127273 15.8759113 3.6230786
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## 1036 7.1127273 6.6170191 5.9357163
## 1037 7.1127273 6.6170191 7.1021421
## 1038 7.1127273 6.6170191 8.1282322
## 1039 7.1127273 6.6170191 6.0001488
## 1040 7.1127273 6.6170191 3.6230786
## 1041 7.1127273 6.6170191 2.4165908
## 1042 7.1127273 5.9357163 7.1021421
## 1043 7.1127273 5.9357163 8.1282322
## 1044 7.1127273 5.9357163 6.0001488
## 1045 7.1127273 5.9357163 3.6230786
## 1046 7.1127273 5.9357163 2.4165908
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## 1048 7.1127273 7.1021421 6.0001488
## 1049 7.1127273 7.1021421 3.6230786
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## 1051 7.1127273 8.1282322 6.0001488
## 1052 7.1127273 8.1282322 3.6230786
## 1053 7.1127273 8.1282322 2.4165908
## 1054 7.1127273 6.0001488 3.6230786
## 1055 7.1127273 6.0001488 2.4165908
## 1056 7.1127273 3.6230786 2.4165908
## 1057 1.0256657 15.8759113 6.6170191
## 1058 1.0256657 15.8759113 5.9357163
## 1059 1.0256657 15.8759113 7.1021421
## 1060 1.0256657 15.8759113 8.1282322
## 1061 1.0256657 15.8759113 6.0001488
## 1062 1.0256657 15.8759113 3.6230786
## 1063 1.0256657 15.8759113 2.4165908
## 1064 1.0256657 6.6170191 5.9357163
## 1065 1.0256657 6.6170191 7.1021421
## 1066 1.0256657 6.6170191 8.1282322
## 1067 1.0256657 6.6170191 6.0001488
## 1068 1.0256657 6.6170191 3.6230786
## 1069 1.0256657 6.6170191 2.4165908
## 1070 1.0256657 5.9357163 7.1021421
## 1071 1.0256657 5.9357163 8.1282322
## 1072 1.0256657 5.9357163 6.0001488
## 1073 1.0256657 5.9357163 3.6230786
## 1074 1.0256657 5.9357163 2.4165908
## 1075 1.0256657 7.1021421 8.1282322
## 1076 1.0256657 7.1021421 6.0001488
## 1077 1.0256657 7.1021421 3.6230786
## 1078 1.0256657 7.1021421 2.4165908
## 1079 1.0256657 8.1282322 6.0001488
## 1080 1.0256657 8.1282322 3.6230786
## 1081 1.0256657 8.1282322 2.4165908
## 1082 1.0256657 6.0001488 3.6230786
## 1083 1.0256657 6.0001488 2.4165908
## 1084 1.0256657 3.6230786 2.4165908
## 1085 15.8759113 6.6170191 5.9357163
## 1086 15.8759113 6.6170191 7.1021421
## 1087 15.8759113 6.6170191 8.1282322
## 1088 15.8759113 6.6170191 6.0001488
## 1089 15.8759113 6.6170191 3.6230786
## 1090 15.8759113 6.6170191 2.4165908
## 1091 15.8759113 5.9357163 7.1021421
## 1092 15.8759113 5.9357163 8.1282322
## 1093 15.8759113 5.9357163 6.0001488
## 1094 15.8759113 5.9357163 3.6230786
## 1095 15.8759113 5.9357163 2.4165908
## 1096 15.8759113 7.1021421 8.1282322
## 1097 15.8759113 7.1021421 6.0001488
## 1098 15.8759113 7.1021421 3.6230786
## 1099 15.8759113 7.1021421 2.4165908
## 1100 15.8759113 8.1282322 6.0001488
## 1101 15.8759113 8.1282322 3.6230786
## 1102 15.8759113 8.1282322 2.4165908
## 1103 15.8759113 6.0001488 3.6230786
## 1104 15.8759113 6.0001488 2.4165908
## 1105 15.8759113 3.6230786 2.4165908
## 1106 6.6170191 5.9357163 7.1021421
## 1107 6.6170191 5.9357163 8.1282322
## 1108 6.6170191 5.9357163 6.0001488
## 1109 6.6170191 5.9357163 3.6230786
## 1110 6.6170191 5.9357163 2.4165908
## 1111 6.6170191 7.1021421 8.1282322
## 1112 6.6170191 7.1021421 6.0001488
## 1113 6.6170191 7.1021421 3.6230786
## 1114 6.6170191 7.1021421 2.4165908
## 1115 6.6170191 8.1282322 6.0001488
## 1116 6.6170191 8.1282322 3.6230786
## 1117 6.6170191 8.1282322 2.4165908
## 1118 6.6170191 6.0001488 3.6230786
## 1119 6.6170191 6.0001488 2.4165908
## 1120 6.6170191 3.6230786 2.4165908
## 1121 5.9357163 7.1021421 8.1282322
## 1122 5.9357163 7.1021421 6.0001488
## 1123 5.9357163 7.1021421 3.6230786
## 1124 5.9357163 7.1021421 2.4165908
## 1125 5.9357163 8.1282322 6.0001488
## 1126 5.9357163 8.1282322 3.6230786
## 1127 5.9357163 8.1282322 2.4165908
## 1128 5.9357163 6.0001488 3.6230786
## 1129 5.9357163 6.0001488 2.4165908
## 1130 5.9357163 3.6230786 2.4165908
## 1131 7.1021421 8.1282322 6.0001488
## 1132 7.1021421 8.1282322 3.6230786
## 1133 7.1021421 8.1282322 2.4165908
## 1134 7.1021421 6.0001488 3.6230786
## 1135 7.1021421 6.0001488 2.4165908
## 1136 7.1021421 3.6230786 2.4165908
## 1137 8.1282322 6.0001488 3.6230786
## 1138 8.1282322 6.0001488 2.4165908
## 1139 8.1282322 3.6230786 2.4165908
## 1140 6.0001488 3.6230786 2.4165908mean_norm1 = matrix(apply(contoh_norm1, 1, mean))
mean_xbar1 = mean(mean_norm1)
var_xbar1 = var(mean_norm1)
n2 = 4
contoh_norm2 = urnsamples(populasi, size = 4, replace = F, ordered = F)
mean_norm2 = matrix(apply(contoh_norm2, 1, mean))
mean_xbar2 = mean(mean_norm2)
var_xbar2 = var(mean_norm2)
n3 = 15
contoh_norm3 = urnsamples(populasi, size = 15, replace = F, ordered = F)
mean_norm3 = matrix(apply(contoh_norm3, 1, mean))
mean_xbar3 = mean(mean_norm3)
var_xbar3 = var(mean_norm3)
hist(mean_norm1,main = paste("(n = 3)"),xlab = "xbar")
hist(mean_norm2,main = paste("(n = 4)"),xlab = "xbar")
hist(mean_norm3,main = paste("(n = 15)"),xlab = "xbar")
hasil = data.frame("."=c("mean","varian"),"Populasi"=c(5,12),"n=3"=c(mean_xbar1,var_xbar1),"n=4"=c(mean_xbar2,var_xbar2),"n=15"=c(mean_xbar3,var_xbar3))
hasil## . Populasi n.3 n.4 n.15
## 1 mean 5 4.809415 4.809415 4.8094152
## 2 varian 12 4.547044 3.207524 0.2672558Penerapan ketakbiasan penduga (mean)
#POPULASI TERHINGGA
#1. Sebaran Normal
library(probs)
set.seed(123)
n = 10
populasi1 = rnorm(20)
mean_pop1 = mean(populasi1)
sampel_normal1 = urnsamples(populasi1, size = 10, replace = F, ordered = F)
mean_normal1 = matrix(apply(sampel_normal1, 1, mean))
median_normal1 = matrix(apply(sampel_normal1, 1, median))
harapan_mean_norm1 = mean(mean_normal1)
harapan_median_norm1 = mean(median_normal1)
#2. Sebaran Eksponensial
library(probs)
set.seed(123)
n = 10
populasi2 = rexp(20)
mean_pop2 = mean(populasi2)
sampel_exp1 = urnsamples(populasi2, size = 10, replace = F, ordered = F)
mean_exp1 = matrix(apply(sampel_exp1, 1, mean))
median_exp1 = matrix(apply(sampel_exp1, 1, median))
harapan_mean_exp1 = mean(mean_exp1)
harapan_median_exp1 = mean(median_exp1)
#3. Uniform
library(probs)
set.seed(123)
n = 10
populasi3 = runif(20)
mean_pop3 = mean(populasi3)
sampel_unif1 = urnsamples(populasi3, size = 10, replace = F, ordered = F)
mean_unif1 = matrix(apply(sampel_unif1, 1, mean))
median_unif1 = matrix(apply(sampel_unif1, 1, median))
harapan_mean_unif1 = mean(mean_unif1)
harapan_median_unif1 = mean(median_unif1)
hasil = data.frame("Hasil"=c("mean_populasi","harapan_mean_contoh","harapan_median_contoh"),"Sebaran Normal"=c(mean_pop1,harapan_mean_norm1,harapan_median_norm1),"Sebaran Eksponensial"=c(mean_pop2,harapan_mean_exp1,harapan_median_exp1),"Sebaran Seragam"=c(mean_pop3,harapan_mean_unif1,harapan_median_unif1))
hasil## Hasil Sebaran.Normal Sebaran.Eksponensial Sebaran.Seragam
## 1 mean_populasi 0.1416238 0.8111726 0.5508084
## 2 harapan_mean_contoh 0.1416238 0.8111726 0.5508084
## 3 harapan_median_contoh 0.1174878 0.4931612 0.5504018Penerapan ketakbiasan penduga (Ragam)
# POPULASI TERHINGGA
#Sebaran Normal
set.seed(888)
n = 10
populasi = rnorm(20)
sigma2 = var(populasi)*(20-1)/20 #fungsi var pada R adalah varian contoh (penyebut n-1) sehingga perlu dikali (n-1)/n
library(probs)
sampel = urnsamples(populasi, size = 10, replace = F, ordered = F)
## Pembagi (n-1)
s2.n1 = matrix(apply(sampel, 1, var))
E.s2.n1 = mean(s2.n1)
## Pembagi (n)
s2.n = s2.n1*(10-1)/10
E.s2.n = mean(s2.n)
#Sebaran Eksponensial
set.seed(888)
n = 10
populasi2 = rexp(20)
sigma2.exp = var(populasi2)*(20-1)/20
library(probs)
sampel_exp = urnsamples(populasi2, size = 10, replace = F, ordered = F)
## Pembagi (n-1)
s2.n1.exp = matrix(apply(sampel_exp, 1, var))
E.s2.n1.exp = mean(s2.n1.exp)
## Pembagi (n)
s2.n.exp = s2.n1.exp*(10-1)/10
E.s2.n.exp = mean(s2.n.exp)
hasil = data.frame( "." = c("ragam populasi","nilai harapan ragam contoh (n-1)","nilai harapan ragam contoh (n)"),
"Sebaran Normal" = c(sigma2, E.s2.n1, E.s2.n),"Sebaran Eksponensial" = c(sigma2.exp, E.s2.n1.exp, E.s2.n.exp))
hasil## . Sebaran.Normal Sebaran.Eksponensial
## 1 ragam populasi 1.298573 1.750903
## 2 nilai harapan ragam contoh (n-1) 1.366919 1.843056
## 3 nilai harapan ragam contoh (n) 1.230227 1.658750Selang Kepercayaan
n1 = 10
k = 100 #ulangan
alpha = 0.05
mu = 50
std = 10
set.seed(123)
sampel.norm1 = matrix(rnorm(n1*k,mu,std),k)
xbar.norm1 = apply(sampel.norm1,1,mean)
s.norm1 = apply(sampel.norm1,1,sd)
SE.norm1 = s.norm1/sqrt(n1)
z.norm1 = qnorm(1-alpha/2)
SK.norm1 = (xbar.norm1-z.norm1*SE.norm1 < mu & mu < xbar.norm1+z.norm1*SE.norm1)
x.norm1 = sum(SK.norm1)/k #proporsi banyaknya SK yang memuat mu
n2 = 30
k = 100 #ulangan
alpha = 0.05
mu = 50
std = 10
set.seed(123)
sampel.norm2 = matrix(rnorm(n2*k,mu,std),k)
xbar.norm2 = apply(sampel.norm2,1,mean)
s.norm2 = apply(sampel.norm2,1,sd)
SE.norm2 = s.norm2/sqrt(n2)
z.norm2 = qnorm(1-alpha/2)
SK.norm2 = (xbar.norm2-z.norm2*SE.norm2 < mu & mu < xbar.norm2+z.norm2*SE.norm2)
x.norm2 = sum(SK.norm2)/k #proporsi banyaknya SK yang memuat mu
n3 = 100
k = 100 #ulangan
alpha = 0.05
mu = 50
std = 10
set.seed(123)
sampel.norm3 = matrix(rnorm(n3*k,mu,std),k)
xbar.norm3 = apply(sampel.norm3,1,mean)
s.norm3 = apply(sampel.norm3,1,sd)
SE.norm3 = s.norm3/sqrt(n3)
z.norm3 = qnorm(1-alpha/2)
SK.norm3 = (xbar.norm3-z.norm3*SE.norm3 < mu & mu < xbar.norm3+z.norm3*SE.norm3)
x.norm3 = sum(SK.norm3)/k #proporsi banyaknya SK yang memuat muhasil = data.frame("n" =c(10,30,100),"Ketepatan SK Sebaran Normal"=c(x.norm1, x.norm2, x.norm3))
hasil## n Ketepatan.SK.Sebaran.Normal
## 1 10 0.93
## 2 30 0.93
## 3 100 0.96matplot(rbind (xbar.norm2-z.norm2*SE.norm2, xbar.norm2+z.norm2*SE.norm2), rbind(1:k,1:k), col=ifelse(SK.norm2,"blue","red"), type = "l", lty = 1,main='Selang Kepercayaan 95% (n=100)', xlab='SK', ylab='banyak ulangan')
abline(v=mu)
library(car)## Warning: package 'car' was built under R version 4.3.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.3.3data("Prestige")
# Menghitung rata-rata
m <- mean(Prestige$income)
m## [1] 6797.902# Menghitung standar error
p <- dim(Prestige)[1]
se <- sd(Prestige$income)/sqrt(p)
se## [1] 420.4089# Menghitung nilai kritis t
tval <- qt(0.975, df=p-1)
# Menghitung interval kepercayaan
cat(paste("KI: [", round(m-tval*se, 2),",",round(m+tval*se,2),"]"))## KI: [ 5963.92 , 7631.88 ]