Let {X 1 , X 2 ,.. ., X 5 } be a random sample from the exponential distribution with rate parameter . (a) Without doing any calculation, do you expect that the sample median of the random sample is more likely to be smaller than or larger than 1/, the (true) mean of the exponential distribution? Explain your answer. (b) Calculate the probability that the sample median of the random sample is larger than the true mean of the exponential distribution. (c) Let Y = P 5 i=1 X i . Derive the distribution of Y using moment generating function. (d) Let W = P n i=1 U i , where U i i.i.d.