Question

Random variables X and Y have the joint PMF px,y(x, y) = { 50^x e^-50 / (x+1)!, x = 0, 1, ...; y = 0, 1, ..., x, 0 otherwise (a) Find the marginal PMF p_x(x). (b) Find the conditional PMF p_y|x(y|x). (c) find the conditional expected value E[Y|X = x]. (d) Express the random variable E[Y|X] as a function of X and use the iterated expectation to find E[Y].

          Random variables X and Y have the joint PMF
px,y(x, y) = {
50^x e^-50 / (x+1)!, x = 0, 1, ...; y = 0, 1, ..., x,
0 otherwise
(a) Find the marginal PMF p_x(x).
(b) Find the conditional PMF p_y|x(y|x).
(c) find the conditional expected value E[Y|X = x].
(d) Express the random variable E[Y|X] as a function of X and use the iterated expectation to find E[Y].

Random variables X and Y have the joint PMF
px,y(x, y) =
50^x e^-50 / (x+1)!, x = 0, 1, ...; y = 0, 1, ..., x,
0 otherwise
(a) Find the marginal PMF px(x).
(b) Find the conditional PMF py|x(y|x).
(c) find the conditional expected value E[Y|X = x].
(d) Express the random variable E[Y|X] as a function of X and use the iterated expectation to find E[Y].

Added by Gregory G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

08/10/2023

Step 1

First, we need to find the marginal PMF $p_X(x)$. We have the joint PMF $p_{XY}(x, y) = \frac{1}{4}x^2y$ for $x = 0, 1, 2$ and $y = 0, 1, 2$. To find the marginal PMF, we sum over all possible values of $y$: $$ p_X(x) = \sum_{y=0}^2 p_{XY}(x, y) = \sum_{y=0}^2 Show more…

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Random variables X have the joint PMF P(X,Y) = 0.1, for X = 2 and Y = y P(X,Y) = 0,1, otherwise Find the marginal PMF P(X=r). Find the conditional PMF P(Y=y|X=r). Find the conditional expected value E(Y|X=r). Express the random variable E[Y|X] as a function of X and use the iterated expectation to find E(Y).