Question

write the code in stata or R or SAS

3, (Extra Credit): Write code to simulate 5000 of these experiments (each with n = 50 flips of the biased coin, taking p 0.3). Calculate your estimate of p for each repeti- tion and calculate your estimate of the variance of your estimate for each repetition 5000 estimates of p.

Answer 1

R code:

x=matrix(0,nrow=5000,ncol=50)
p_hat=1:5000
var_hat=1:5000
for(i in 1:5000)
{
for(j in 1:50)
{
x[i,j]=rbinom(1,1,0.3)
}
p_hat[i]=mean(x[i,])
var_hat[i]=var(x[i,])
}
mean(var_hat) # average of 5000 variance estimates
var(p_hat) # empirical variance of 5000 estimates of p

Out put:

mean(var_hat)
[1] 0.210412
> var(p_hat)
[1] 0.004267701

Here we observe that average of 5000 variance estimates>empirical variance of 5000 estimates of p.