\({X_1},\;...,\;{X_{100}}\) are independent random samples from the F-distribution with degrees of freedom 3 and 12.
- What is the probability that the sample mean \(\bar X\) is greater than 1.5?
Use the F-distribution formula to find the mean and variance for each random variable.
Then apply the Central Limit Theorem (CLT) to calculate the probability.
- 0.0082
This is calculated with the following R commands
F.mean<-12/(12-2)
F.var<- 2*12^2*(3+12-2)/3/10^2/8
1-pnorm(1.5,mean=F.mean,sd=sqrt(F.var/100))