Question

Suppose X and Y are 2 discrete random variables. Given the PMF of Y conditional on X, and the marginal PMF of X: y | 1 | 2 PY|X=1(y) | 0.2 | 0.8 PY|X=2(y) | 0.3 | 0.7 PY|X=3(y) | 0.5 | 0.5 x | 1 | 2 | 3 P(x = x) | 0.2 | 0.4 | 0.4 (a) Find and tabulate the joint PMF of X and Y (b) Find E(X^2), E(Y) (c) Find E(X^2Y), Cov(X^2,Y) (d) Find and tabulate the conditional probability P_X|Y = 1(x), for x = 1,2,3 (e) Find E(X|Y = 1), Var(X|Y = 1)

          Suppose X and Y are 2 discrete random variables. Given the PMF of Y conditional on X, and the marginal PMF of X:

y | 1 | 2
PY|X=1(y) | 0.2 | 0.8
PY|X=2(y) | 0.3 | 0.7
PY|X=3(y) | 0.5 | 0.5

x | 1 | 2 | 3
P(x = x) | 0.2 | 0.4 | 0.4

(a) Find and tabulate the joint PMF of X and Y
(b) Find E(X^2), E(Y)
(c) Find E(X^2Y), Cov(X^2,Y)
(d) Find and tabulate the conditional probability P_X|Y = 1(x), for x = 1,2,3
(e) Find E(X|Y = 1), Var(X|Y = 1)

Suppose X and Y are 2 discrete random variables. Given the PMF of Y conditional on X, and the marginal PMF of X:

y | 1 | 2
PY|X=1(y) | 0.2 | 0.8
PY|X=2(y) | 0.3 | 0.7
PY|X=3(y) | 0.5 | 0.5

x | 1 | 2 | 3
P(x = x) | 0.2 | 0.4 | 0.4

(a) Find and tabulate the joint PMF of X and Y
(b) Find E(X^2), E(Y)
(c) Find E(X^2Y), Cov(X^2,Y)
(d) Find and tabulate the conditional probability PX|Y = 1(x), for x = 1,2,3
(e) Find E(X|Y = 1), Var(X|Y = 1)

Added by Michael C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

09/28/2022

Step 1

2/0.8 - P(Y=1|X=2) = 0.3/0.7 - P(Y=1|X=3) = 0.5/0.5 - P(X=1) = 0.2 - P(X=2) = 0.4 - P(X=3) = 0.4 We can calculate the joint PMF of X and Y by multiplying the conditional probabilities with the marginal probabilities: P(X=1, Y=1) = P(Y=1|X=1) * P(X=1) = 0.2/0.8 * Show more…

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Suppose X and Y are 2 discrete random variables. Given the PMF of Y conditional on X, and the marginal PMF of X: (a) Find and tabulate the joint PMF of X and Y (b) Find E(X^2), E(Y) (c) Find E(X^2Y), Cov(X^2,Y) (d) Find and tabulate the conditional probability P_X|Y = 1(x), for x = 1,2,3 (e) Find E(X|Y = 1), Var(X|Y = 1)