STAT3110 STATISTICAL INFERENCE

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STAT6110 STAT3110 STATISTICAL INFERENCE
Question 1. Consider a sample of n > 2 independent and identically distributed random variables 1 K. from an exp(A) distribution with probability density function
We will use the notation 0 =
In this assignment you are given the following 2 facts:
(1) Let S„„ = q 1Y, be the sum of n independent exp(A) random variables. Then ST, has a Gamma distribution, Gamma(n. A), which has probability density function An3Y1 1 exP( — As)
s>0 A>0 n>1.
(2) If S Garnma(n, A) then E(71) — A Var(1) (for > 2). —1) — (r. -1)2( _ 2)
Answer the questions on the following page.
1

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