(a) What is the value of the constant c? (b) What is P(Y < X)? (c) What is P(Y > X)? (d) What is P(Y = X)? (e) What is P(Y = 3)? (f) Find the marginal PMFS px(x) and py (y). (g) Find the expectations E[X], E[Y] and E[XY]. (h) Find the variances Var(X), Var(Y) and Var(X +Y). (i) Let A denote the event X > Y. Find E[X | A] and Var(X | A)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 9E
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Random variables X and Y have the joint PMF
c(x² + y²),
| 0,
if x E {1,2, 4} and y E {1,3}
fx,y (x, y) =
otherwise
(a) What is the value of the constant c?
(b) What is P(Y < X)?
(c) What is P(Y > X)?
(d) What is P(Y = X)?
(e) What is P(Y = 3)?
(f) Find the marginal PMFS px(x) and py (y).
(g) Find the expectations E[X], E[Y] and E[XY].
(h) Find the variances Var(X), Var(Y) and Var(X +Y).
(i) Let A denote the event X > Y. Find E[X | A] and Var(X | A)
Transcribed Image Text:Random variables X and Y have the joint PMF c(x² + y²), | 0, if x E {1,2, 4} and y E {1,3} fx,y (x, y) = otherwise (a) What is the value of the constant c? (b) What is P(Y < X)? (c) What is P(Y > X)? (d) What is P(Y = X)? (e) What is P(Y = 3)? (f) Find the marginal PMFS px(x) and py (y). (g) Find the expectations E[X], E[Y] and E[XY]. (h) Find the variances Var(X), Var(Y) and Var(X +Y). (i) Let A denote the event X > Y. Find E[X | A] and Var(X | A)
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