e=exp(1)
e
## [1] 2.718282
pi
## [1] 3.141593
media=170
desv=5
x=170
Calcular la función de densidad f(x) de una distribucion normal
cuando x tiene valor especifico
numerador <- e^(-(x - media)^2 / (2 * desv^2))
denominador <- desv * sqrt(2 * pi)
prob <- numerador / denominador
prob
## [1] 0.07978846
Calcular la probabilidad acumulada F(x) con la funcion de dnorm
dnorm(x = 150:200,mean = media,sd = desv)
## [1] 2.676605e-05 5.838939e-05 1.223804e-04 2.464438e-04 4.768176e-04
## [6] 8.863697e-04 1.583090e-03 2.716594e-03 4.478906e-03 7.094919e-03
## [11] 1.079819e-02 1.579003e-02 2.218417e-02 2.994549e-02 3.883721e-02
## [16] 4.839414e-02 5.793831e-02 6.664492e-02 7.365403e-02 7.820854e-02
## [21] 7.978846e-02 7.820854e-02 7.365403e-02 6.664492e-02 5.793831e-02
## [26] 4.839414e-02 3.883721e-02 2.994549e-02 2.218417e-02 1.579003e-02
## [31] 1.079819e-02 7.094919e-03 4.478906e-03 2.716594e-03 1.583090e-03
## [36] 8.863697e-04 4.768176e-04 2.464438e-04 1.223804e-04 5.838939e-05
## [41] 2.676605e-05 1.178861e-05 4.988494e-06 2.028170e-06 7.922598e-07
## [46] 2.973439e-07 1.072207e-07 3.714724e-08 1.236524e-08 3.954639e-09
## [51] 1.215177e-09
Crear un data.frame con los valores de x y su densidad
datos=data.frame(x=150:200,f.x=dnorm(x = 150:200,mean = media,sd = desv))
datos
## x f.x
## 1 150 2.676605e-05
## 2 151 5.838939e-05
## 3 152 1.223804e-04
## 4 153 2.464438e-04
## 5 154 4.768176e-04
## 6 155 8.863697e-04
## 7 156 1.583090e-03
## 8 157 2.716594e-03
## 9 158 4.478906e-03
## 10 159 7.094919e-03
## 11 160 1.079819e-02
## 12 161 1.579003e-02
## 13 162 2.218417e-02
## 14 163 2.994549e-02
## 15 164 3.883721e-02
## 16 165 4.839414e-02
## 17 166 5.793831e-02
## 18 167 6.664492e-02
## 19 168 7.365403e-02
## 20 169 7.820854e-02
## 21 170 7.978846e-02
## 22 171 7.820854e-02
## 23 172 7.365403e-02
## 24 173 6.664492e-02
## 25 174 5.793831e-02
## 26 175 4.839414e-02
## 27 176 3.883721e-02
## 28 177 2.994549e-02
## 29 178 2.218417e-02
## 30 179 1.579003e-02
## 31 180 1.079819e-02
## 32 181 7.094919e-03
## 33 182 4.478906e-03
## 34 183 2.716594e-03
## 35 184 1.583090e-03
## 36 185 8.863697e-04
## 37 186 4.768176e-04
## 38 187 2.464438e-04
## 39 188 1.223804e-04
## 40 189 5.838939e-05
## 41 190 2.676605e-05
## 42 191 1.178861e-05
## 43 192 4.988494e-06
## 44 193 2.028170e-06
## 45 194 7.922598e-07
## 46 195 2.973439e-07
## 47 196 1.072207e-07
## 48 197 3.714724e-08
## 49 198 1.236524e-08
## 50 199 3.954639e-09
## 51 200 1.215177e-09
Graficar la densidad con gplot
library(ggplot2)
ggplot(data = datos,aes(x = x,y=f.x))+
geom_point(color="pink")+
geom_line(color="violet")
Calcular probabilidades acumuladas con pnorm
Probabilidad acumulada con personas que miden 160
acum=pnorm(q = 160,mean = media,sd = desv)
acum
## [1] 0.02275013
Agregar el valor acumulado a data_frame
datos=data.frame(x=150:200,f.x=dnorm(x = 150:200,mean = media,sd = desv),
F.x=pnorm(q=150:200,mean=media,sd=desv))
datos
## x f.x F.x
## 1 150 2.676605e-05 3.167124e-05
## 2 151 5.838939e-05 7.234804e-05
## 3 152 1.223804e-04 1.591086e-04
## 4 153 2.464438e-04 3.369293e-04
## 5 154 4.768176e-04 6.871379e-04
## 6 155 8.863697e-04 1.349898e-03
## 7 156 1.583090e-03 2.555130e-03
## 8 157 2.716594e-03 4.661188e-03
## 9 158 4.478906e-03 8.197536e-03
## 10 159 7.094919e-03 1.390345e-02
## 11 160 1.079819e-02 2.275013e-02
## 12 161 1.579003e-02 3.593032e-02
## 13 162 2.218417e-02 5.479929e-02
## 14 163 2.994549e-02 8.075666e-02
## 15 164 3.883721e-02 1.150697e-01
## 16 165 4.839414e-02 1.586553e-01
## 17 166 5.793831e-02 2.118554e-01
## 18 167 6.664492e-02 2.742531e-01
## 19 168 7.365403e-02 3.445783e-01
## 20 169 7.820854e-02 4.207403e-01
## 21 170 7.978846e-02 5.000000e-01
## 22 171 7.820854e-02 5.792597e-01
## 23 172 7.365403e-02 6.554217e-01
## 24 173 6.664492e-02 7.257469e-01
## 25 174 5.793831e-02 7.881446e-01
## 26 175 4.839414e-02 8.413447e-01
## 27 176 3.883721e-02 8.849303e-01
## 28 177 2.994549e-02 9.192433e-01
## 29 178 2.218417e-02 9.452007e-01
## 30 179 1.579003e-02 9.640697e-01
## 31 180 1.079819e-02 9.772499e-01
## 32 181 7.094919e-03 9.860966e-01
## 33 182 4.478906e-03 9.918025e-01
## 34 183 2.716594e-03 9.953388e-01
## 35 184 1.583090e-03 9.974449e-01
## 36 185 8.863697e-04 9.986501e-01
## 37 186 4.768176e-04 9.993129e-01
## 38 187 2.464438e-04 9.996631e-01
## 39 188 1.223804e-04 9.998409e-01
## 40 189 5.838939e-05 9.999277e-01
## 41 190 2.676605e-05 9.999683e-01
## 42 191 1.178861e-05 9.999867e-01
## 43 192 4.988494e-06 9.999946e-01
## 44 193 2.028170e-06 9.999979e-01
## 45 194 7.922598e-07 9.999992e-01
## 46 195 2.973439e-07 9.999997e-01
## 47 196 1.072207e-07 9.999999e-01
## 48 197 3.714724e-08 1.000000e+00
## 49 198 1.236524e-08 1.000000e+00
## 50 199 3.954639e-09 1.000000e+00
## 51 200 1.215177e-09 1.000000e+00
Calcular la probabilidad mayor o gial a 160, cola por la
derecha
pnorm(q=160,mean=media,sd=desv,lower.tail = FALSE)
## [1] 0.9772499
1-pnorm(q=160,mean=media,sd=desv)
## [1] 0.9772499
Generar numeros aleatorios de una distribucion normal
estaturas=rnorm(n = 100,mean = media,sd=desv)
estaturas
## [1] 164.7727 178.7097 170.7548 177.9564 164.9955 170.1224 168.4776 161.8887
## [9] 171.9715 170.3433 171.2443 169.7881 175.6434 167.1450 165.2918 162.5984
## [17] 172.0749 163.0767 174.1985 181.4053 177.7694 157.8936 173.9288 163.9575
## [25] 166.0523 173.0345 167.2201 163.3442 164.9568 171.3589 175.3700 163.8394
## [33] 163.3908 165.8084 171.8055 172.5824 162.8515 170.2655 169.8004 176.4497
## [41] 168.3523 172.1154 169.2478 180.5676 178.8331 160.9864 163.7371 180.0565
## [49] 171.0034 176.9095 174.2565 165.6787 167.2669 176.1860 169.2000 167.2831
## [57] 174.0692 171.6099 165.2482 168.2423 169.5714 172.5511 173.1706 177.9164
## [65] 165.2925 171.3326 164.7710 177.0656 174.1238 167.9852 170.7354 162.0618
## [73] 171.5535 169.0428 167.4721 170.7668 168.5696 170.1441 157.1175 165.8335
## [81] 177.1944 170.6340 165.6242 170.0711 167.6103 166.9689 166.6193 160.8712
## [89] 166.5519 167.1238 179.8170 168.5765 168.5284 165.7601 163.4283 168.3290
## [97] 167.8504 170.9347 166.2053 160.0266
mean(estaturas)
## [1] 169.4079
Obtener el valor x a partir de un acumulada
qnorm(p = .5,mean = media,sd=desv)
## [1] 170