HW Week 3

Problem 3.5.1

Part a)

set.seed(42)
dice1<-sample(1:6,500,replace=TRUE)
set.seed(43)
dice2<-sample(1:6,500,replace=TRUE)

dsum<-dice1+dice2

summary(dsum)

Part b)

set.seed(42)
p1<-c(1,2,3,4,5,6)
p2<-c(1,1,1,3,1,1)
dice1<-sample(1:6,500,replace=TRUE,prob=p1)
set.seed(43)
dice2<-sample(1:6,500,replace=TRUE,prob=p2)

dsum<-dice1+dice2

summary(dsum)

Part c)

set.seed(42)
dice1<-sample(1:6,10000,replace=TRUE)
set.seed(43)
dice2<-sample(1:6,10000,replace=TRUE)

dsum<-dice1+dice2
dsum<-data.frame(dsum)
summary(dsum)

##       dsum       
##  Min.   : 2.000  
##  1st Qu.: 5.000  
##  Median : 7.000  
##  Mean   : 6.985  
##  3rd Qu.: 9.000  
##  Max.   :12.000

library("plyr")


mcfreq<-data.frame(count(dsum))
trueprob<-c(1,2,3,4,5,6,5,4,3,2,1)/36
mcprob<-data.frame("simprob"=mcfreq$freq/10000)

###compare differences (percent of true values)

abs(trueprob-mcprob)/trueprob*100

##    simprob
## 1    9.440
## 2    4.420
## 3    5.360
## 4    1.540
## 5    1.144
## 6    0.440
## 7    0.136
## 8    2.260
## 9    0.200
## 10   2.240
## 11   2.800

Problem 3.5.5

zz1z Separately attached,

Problem 3.5.17

Item<-c("Oats","Peas","Beans","Barley")
cost<-c(1.05,3.17,1.99,.95)
sell<-c(1.29,3.76,2.23,1.65)
maxD<-c(10,8,14,11)
data<-data.frame(Item,cost,sell,maxD)

trueD_90<-c()
TotalC<-c()
TotalP<-c()
TotalR<-c()

for(i in 1:10000) {

trueD_90<-c(sum(round(runif(90,0,data$maxD[1]),0)),sum(round(runif(90,0,data$maxD[2]),0)),sum(round(runif(90,0,data$maxD[3]),0)),sum(round(runif(90,0,data$maxD[4]),0)))

TotalC[i]<-sum(data$cost*trueD_90)
TotalR[i]<-sum(data$sell*trueD_90)
TotalP[i]<-sum(TotalR[i]-TotalC[i])

}

##Histogram of Costs
summary(TotalC)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2915    3262    3337    3336    3410    3713

hist(TotalC)

#Normal

## Revenue
summary(TotalR)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    3653    4064    4154    4154    4246    4637

hist(TotalR)

## Profit

summary(TotalP)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   707.9   799.5   817.9   817.9   836.6   924.1

hist(TotalP)