(d) Find P(1 Y ≤ 3|X= 1), P(Y ≤ 2|X ≤ P(X=2|Y= 3). (e) Find E(Y|X= 1) and Var(Y|X=1). H 2), and
(d) Find P(1 Y ≤ 3|X= 1), P(Y ≤ 2|X ≤ P(X=2|Y= 3). (e) Find E(Y|X= 1) and Var(Y|X=1). H 2), and
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Need help with ONLY parts (d) and (e) Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable.
Transcribed Image Text:4.3-1. Let X and Y have the joint pmf
x +
f(x, y) = 32
x = 1,2, y = 1,2,3,4.
(a) Display the joint pmf and the marginal pmfs on a graph
like Figure 4.3-1(a).
(b) Find g(xly) and draw a figure like Figure 4.3-1(b).
depicting the conditional pmfs for y= 1, 2, 3, and 4.
(c) Find h(y|x) and draw a figure like Figure 4.3-1(c),
depicting the conditional pmfs for x = 1 and 2.
(d) Find P(1 ≤ y ≤ 3)X = 1), P(Y ≤ 2 X = 2), and
P(X=21Y = 3).
(e) Find E(Y|X= 1) and Var(Y|X = 1).
Transcribed Image Text:4.3-1 (a) fx(x) = (4x+10)/32, x = 1.2; fy(v) (3 +
2y)/32, y = 1,2,3,4;
(b) g(x y) = (x+y)/(3+2y), x= 1, 2, y = 1, 2, 3, 4;
(c) h(y|x) = (x+y)/(4x+10), y = 1, 2, 3, 4, x= 1,2;
(d) 9/14, 7/18, 5/9; (e) 20/7, 55/49.
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