Consider the joint pdf of the random variables X and Y : 1/8, if 0 ≤...

Question

Question

Consider the joint pdf of the random variables X and Y :
1/8, if 0 ≤ y ≤ 4, y ≤ x ≤ y + 2

f (x, y) = 0, otherwise

(i) Draw the region where f (x, y) ̸= 0. Shade its area.

(ii) Compute the probability P (X + Y ≤ 2).

(iii) Compute the marginal pdf f1(x) of X. Specify clearly its support, i.e., the subset of the real line such that f1(x) ̸= 0.

(iv) Compute the marginal pdf f2(y) of Y . Specify clearly its support, i.e., the subset of the real line such that f2(y) ̸= 0.

Answer 1

Answer #1

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Answer 2

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