1. (15 points) Suppose that X₁ and X₂ constitute a sample of size 2 from a population in which a typical value X is equa

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1 15 Points Suppose That X And X Constitute A Sample Of Size 2 From A Population In Which A Typical Value X Is Equa 1 (35.66 KiB) Viewed 32 times

1. (15 points) Suppose that X₁ and X₂ constitute a sample of size 2 from a population in which a typical value X is equal to either 1 or 2 with respective probabilities P(X= 1) = 0.7 P(X= 2) = 0.3 (a) What are the possible values of X = (X₁ + X₂)/2? (b) Determine the probabilities that X assumes the values in (a). (c) Using (b), directly compute E[X] and Var (X). = (d) Are your answers to (c) consistent with the general formula that E[X] = μ and Var (X) = o2/n, where μ :=) E[X] and o² = Var (X). :=