Question

2) We know that the variance of mean of a Poisson distributed population are e Thus we can u the sample me an or the sample variance to estim ate the population mean (or variance) of s population which has a Poisson distribution Construct a simulation th at wil compare the two estim ators

Answer 1

R code:

n=10000
x=matrix(0,nrow=n,ncol=10)
m=1:n*0
var=1:n*0
for(i in 1:n)
{
x[i,]=rpois(10,lambda=2)
m[i]=mean(x[i,])
var[i]=var(x[i,])
}
M=mean(m)
Var=mean(var)
M
Var

Output:

> M
[1] 1.99852
> Var
[1] 1.999093

Description: We draw a sample of size 10 from Poisson(2) and compute sample mean and sample variance. We repeat this whole process 10000 times and compute 10000 sample mean and sample standard deviation then we take average these 10000 sample means and variances then we observe that these average values are very closed to true value of lambda i.e. 2.

However here we observe that sample mean is closer to 2 than sample variance.