Let X1, X2, X3 be independent random variables with E(X1) = 1, E(X2) = 2 and...

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Question

Let X1, X2, X3 be independent random variables with E(X1) = 1, E(X2) = 2 and E(X3) = 3. Let Y = 3X1 − 2X2 + X3. Find E(Y ), Var(Y ) in the following examples.
1. X1, X2, X3 are Poisson. [Recall that the variance of Poisson(λ) is λ.]
2. X1, X2, X3 are normal, with respective variances σ12 = 1, σ2 = 3, σ32 = 5. Find P(0 ≤ Y ≤ 5).
  
  [Recall that any linear combination of independent normal random variables also is normal.]

Answer 1

Answer #1

Answer 2

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