Just for testing
Q3
(ignore issue descriptions)
set.seed(123)
unfair.dice.probs = rep((1-0.25)/5, 6)
unfair.dice.probs[2] = 0.25
sample(c(1,2,3,4,5,6), 2, prob=unfair.dice.probs, replace=TRUE)## [1] 3 6sim.times = 1:10000
result = matrix(NA,
ncol=1, nrow=length(sim.times))
dim(result)## [1] 10000 1rownames(result) = sim.times
for (i in sim.times) {
dice.fair = sample(c(1,2,3,4,5,6), 2, replace=TRUE)
dice.unfair = sample(c(1,2,3,4,5,6), 1, prob=unfair.dice.probs, replace=TRUE)
result[i] = min(dice.fair[1], dice.fair[2], dice.unfair)
}
cat("Expected value: ", mean(result), "\nAns:", round(mean(result)))## Expected value: 2.0065
## Ans: 2Q4
(ignore issue descriptions)
set.seed(486)
highSkill = 0.5
lowSkill = 1 - highSkill
getSales.highSkill = 2/3
notGetSales.highSkill = 1 - getSales.highSkill
getSales.lowSkill = 1/3
notGetSales.lowSkill = 1 - getSales.lowSkill
getsales.sim=function(n=20){
simulate.list=rep(NA, n)
highOrLow=sample(c(1, -1),
1,
prob=c(highSkill, lowSkill),
replace=TRUE)
if(highOrLow==1) {
simulate.list=
sample(c("getSales.highSkill", "notGetSales.highSkill"),
n,
prob=c(getSales.highSkill, notGetSales.highSkill),
replace=TRUE)
}
else if (highOrLow==-1) {
simulate.list=
sample(c("getSales.lowSkill", "notGetSales.lowSkill"),
n,
prob=c(getSales.lowSkill, notGetSales.lowSkill),
replace=TRUE)
}
simulate.list
}
getsales.sim()## [1] "notGetSales.lowSkill" "notGetSales.lowSkill" "notGetSales.lowSkill"
## [4] "notGetSales.lowSkill" "notGetSales.lowSkill" "notGetSales.lowSkill"
## [7] "notGetSales.lowSkill" "notGetSales.lowSkill" "notGetSales.lowSkill"
## [10] "notGetSales.lowSkill" "getSales.lowSkill" "getSales.lowSkill"
## [13] "getSales.lowSkill" "getSales.lowSkill" "notGetSales.lowSkill"
## [16] "notGetSales.lowSkill" "getSales.lowSkill" "notGetSales.lowSkill"
## [19] "notGetSales.lowSkill" "getSales.lowSkill"S = 1000
getsales.sim.table=replicate(S, getsales.sim())
dim(getsales.sim.table)## [1] 20 1000num.highSkill=c()
num.getSales.highSkill=c()
num.notGetSales.highSkill=c()
num.lowSkill=c()
num.getSales.lowSkill=c()
num.notGetSales.lowSkill=c()
num.getSales=c()
num.notGetSales=c()
for(i in 1:ncol(getsales.sim.table)) {
num.getSales.highSkill[i]=sum(getsales.sim.table[,i]=="getSales.highSkill")
num.notGetSales.highSkill[i]=sum(getsales.sim.table[,i]=="notGetSales.highSkill")
num.getSales.lowSkill[i]=sum(getsales.sim.table[,i]=="getSales.lowSkill")
num.notGetSales.lowSkill[i]=sum(getsales.sim.table[,i]=="notGetSales.lowSkill")
num.highSkill[i]=sum(getsales.sim.table[,i]=="getSales.highSkill")+
sum(getsales.sim.table[,i]=="notGetSales.highSkill")
num.highSkill[which(num.highSkill>0)]=1
num.lowSkill[i]=sum(getsales.sim.table[,i]=="getSales.lowSkill")+
sum(getsales.sim.table[,i]=="notGetSales.lowSkill")
num.lowSkill[which(num.lowSkill>0)]=1
num.getSales[i]=sum(getsales.sim.table[,i]=="getSales.highSkill")+
sum(getsales.sim.table[,i]=="getSales.lowSkill")
num.notGetSales[i]=sum(getsales.sim.table[,i]=="notGetSales.highSkill")+
sum(getsales.sim.table[,i]=="notGetSales.lowSkill")
}
k=9
ans.1 = sum(num.getSales>=k)/S
ans.2 = sum(num.getSales.highSkill>=k)/sum(num.highSkill)
ans.3 = sum(num.getSales.highSkill>=k)/sum(num.getSales>=k)
cat("A1: ", ans.1)## A1: 0.583# P(get promoted | high skill)
cat("A2: ", ans.2)## A2: 0.9902153cat("A3: ", ans.3)## A3: 0.8679245prob.table = matrix(NA,
ncol = 3, nrow = 20)
rownames(prob.table) = seq(1, 20, 1)
colnames(prob.table) = c("P(promoted)", "P(promoted | high skill)", "P(promoted with high skill | promoted)")
for (threshold in 1:20) {
prob.table[threshold, 1] = sum(num.getSales>=threshold)/S
prob.table[threshold, 2] = sum(num.getSales.highSkill>=threshold)/sum(num.highSkill)
prob.table[threshold, 3] = sum(num.getSales.highSkill>=threshold)/sum(num.getSales>=threshold)
}; prob.table## P(promoted) P(promoted | high skill) P(promoted with high skill | promoted)
## 1 1.000 1.000000000 0.5110000
## 2 0.998 1.000000000 0.5120240
## 3 0.990 1.000000000 0.5161616
## 4 0.974 1.000000000 0.5246407
## 5 0.930 1.000000000 0.5494624
## 6 0.862 1.000000000 0.5928074
## 7 0.765 0.998043053 0.6666667
## 8 0.663 0.998043053 0.7692308
## 9 0.583 0.990215264 0.8679245
## 10 0.535 0.968688845 0.9252336
## 11 0.491 0.935420744 0.9735234
## 12 0.438 0.845401174 0.9863014
## 13 0.349 0.681017613 0.9971347
## 14 0.253 0.495107632 1.0000000
## 15 0.157 0.307240705 1.0000000
## 16 0.081 0.158512720 1.0000000
## 17 0.038 0.074363992 1.0000000
## 18 0.016 0.031311155 1.0000000
## 19 0.003 0.005870841 1.0000000
## 20 0.000 0.000000000 NaNQ5
set.seed(89898)
p.return.dayofweek = seq(0.1, 0.4, 0.1)
p.return.origin.lib = 0.5
p.return.foreign.lib = 1 - p.return.origin.lib
sim.returnBook = function() {
return.lib = sample(c("origin.lib", "foreign.lib"), 1, replace=T)
if (return.lib == "origin.lib") {
return.dayofweek = sample(c("Mon.", "Tue.", "Wed.", "Thu."),
1,
prob=p.return.dayofweek,
replace=T)
}
else {
return.dayofweek = sample(c("Wed.", "Thu.", "Fri.", "Sat."),
1,
prob=p.return.dayofweek,
replace=T)
}
return(return.dayofweek)
}
sim.returnBook()## [1] "Thu."sim.times = 1000
sim.recordTable = replicate(sim.times, sim.returnBook())
#return.Wed = c()
#for (i in 1:sim.times) {
# return.Wed[i] = sum(sim.recordTable[i]=="Wed.")
#}
#sum(return.Wed==1)/sim.times
num.return.Wed = length(sim.recordTable[which(sim.recordTable=="Wed.")])
cat(num.return.Wed/sim.times)## 0.214Including Plots
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