Stat 200 Lab 4

Problem 1

result<-matrix(0,nrow=5000,ncol=8) 
result1<-sample(c(0,0,0,0,0,0,1,1,1,1), size=8,replace =T)
for(i in 1:5000){result[i,]<-sample(c(0,0,0,0,0,0,1,1,1,1), size=8,replace =T)} 
Rowsum<-rowSums(result)
round(table(Rowsum)/5000,3)

## Rowsum
##     0     1     2     3     4     5     6     7     8 
## 0.015 0.094 0.205 0.282 0.236 0.121 0.040 0.007 0.000

#let's look at the theoretical distribution
round(dbinom(0:8, size=8, prob=0.4),3)

## [1] 0.017 0.090 0.209 0.279 0.232 0.124 0.041 0.008 0.001

barplot(round(table(Rowsum)/5000,3),main = 'Experimental Binomial Distribution')

barplot(round(dbinom(0:8, size=8, prob=0.4),3),names.arg = 0:8,main = 'Theoretical Binomial Distribution')

Problem 2

Poisson<-rpois(3000,2.3)
barplot(round(table(Poisson)/3000,3),main = 'Experimental Poisson Distribution')

barplot(round(dpois(0:10, lambda = 2.3),3),names.arg = 0:10,main = 'Theoretical Poisson Distribution')