1.Suppose that ₁, ₂, ... are i.i.d RV drawn from a normal distribution N(1,5) distribution.You compute the sample average.

a.Find the expected value of the sample average and the variance of sample average for each of the following cases i) n=20, ii) n=200, and iii) n=2000.

b.What is the asymptotic distribution of the sample average for each of the following cases i) n=20, ii) n=200, and iii) n=2000.

c.Sketch the probability density of sample average for i.) n=20, ii) n=200, and iii) n=2000.Explain what happens to the probability density as you increase the number of observations?