(Solution) - A population has distribution Value Probability 1 6 3 -(2025 Original AI-Free Solution)

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A population has distribution
Value Probability
1....................... .6
3....................... .3
5....................... .1
Let X1 and X2 be independent and each have the same distribution as the population.
(a) Determine the missing elements in the table for the sampling distribution of = (X1 + X2)/2.

(b) Find the expected value of .
(c) If the sample size is increased to 25, give the mean and variance of .