Question

1. The joint pmf of two random variables X and Y is given by $p_{x,y}(x, y) = \begin{cases} \frac{1}{30}(2x + y) & x = 1,2; y = 1,2,3 \\ 0 & \text{elsewhere} \end{cases}$ (a) Find E[Y|X = x] and E[X|Y = y]. (b) Find E[Y] and E[X], using the results of part (a).

          1. The joint pmf of two random variables X and Y is given by
$p_{x,y}(x, y) = \begin{cases} \frac{1}{30}(2x + y) & x = 1,2; y = 1,2,3 \\ 0 & \text{elsewhere} \end{cases}$
(a) Find E[Y|X = x] and E[X|Y = y].
(b) Find E[Y] and E[X], using the results of part (a).

1. The joint pmf of two random variables X and Y is given by
px,y(x, y) = (1)/(30)(2x + y) x = 1,2; y = 1,2,3
0 elsewhere
(a) Find E[Y|X = x] and E[X|Y = y].
(b) Find E[Y] and E[X], using the results of part (a).

Added by Shannon M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

04/26/2023

Step 1

For x = 1: E[Y|X = 1] = Σ y * P(Y = y|X = 1) = 1 * P(Y = 1|X = 1) + 2 * P(Y = 2|X = 1) + 3 * P(Y = 3|X = 1) = 1 * (2(1) + 1) / 30 + 2 * (2(1) + 1) / 30 + 3 * (2(1) + 1) / 30 = 1 * 3/30 + 2 * 5/30 + 3 * 7/30 = 3/30 + Show more…

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1. The joint pmf of two random variables X and Y is given by (2x + y) 30 C0 x = 1,2; y = 1,2,3 elsewhere. (a) Find E[Y|X = x] and E[X|Y = y] (b) Find E[Y] and E|X], using the results of part (a)