question archive Suppose that X1,
Suppose that X1,
Subject:MathPrice: Bought3
Suppose that X1, . . . , Xn form a random sample of exponential random variables all with rate λ.
a) (5 points) Explain what the sampling distribution of X bar = Summation from i=1 to n of Xi/n represents.
b) (5 points) Note that the sum of independent and identically distributed exponential random variables has a gamma distribution. Specifically, if S = Summation from i=1 to n of Xi, then S follows a gamma distribution with parameters α = n and β = 1/λ. Use this fact to find the sampling distribution of X bar.
c) (5 points) Describe how the skewness of the sampling distribution changes as n increases. Does the result surprise you? Justify your answer.
