Question

A = {1, 2} and B = {α, β, δ}

Find B x P(A)

where P(A) is the power set multiplied by cross product of B.

I know that P(A) = {∅, {1}, {2}, {1, 2}}

Explanations along with the answer would be helpful! Thanks

Answer #1

Let X ∼ Beta(α, β).
(a) Show that EX 2 = (α + 1)α (α + β + 1)(α + β) .
(b) Use the fact that EX = α/(α + β) and your answer to the
previous part to show that Var X = αβ (α + β) 2 (α + β + 1).
(c) Suppose X is the proportion of free-throws made over the
lifetime of a randomly sampled kid, and assume that X ∼ Beta(2,
8)
....

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4. Let X1. ..., Xn, be a random sample from Exponential(β) with
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α and β are two parameters. (a) (2.5 marks) Does y exhibits
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