Q3 With the exponential distribution in Q2, use rexp() from R, draw a sample of N = 10. (3) Compute the biased estimator (W 72) and unbiased estimator (( 72)) of V(X). Compare to E(X2) E(X)2 from Q2. (b) How would your results change if N = 1000? Q2 (You could list the equation and let R do the integral. ) 8.6 The random variable X has the exponential distribution with parameter ) = 2. (a) Use the definite integral formula - "Ped dt = n!/a"t! for a > 0 and n positive integer, to show that E(X) = 1/2, E(X2) = 1/2, E(X3) = 3/4, E(X') = 3/2. (b) Consider random sampling, sample size 20, from this population, and let T = (X, + . . . + X3)/20. Calculate E(T) and V(T)