4.3-1. Let X and Y have the joint pmf 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). f(x, y) = (b) Find g(x y) and draw a figure like Figure 4.3-1(b), depicting the conditional pmfs for y= 1, 2, 3, and 4. (e) Find h(y|x) and draw a figure like Figure 4.3-1(c), depicting the conditional pmfs for x = 1 and 2.
4.3-1. Let X and Y have the joint pmf 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). f(x, y) = (b) Find g(x y) and draw a figure like Figure 4.3-1(b), depicting the conditional pmfs for y= 1, 2, 3, and 4. (e) Find h(y|x) and draw a figure like Figure 4.3-1(c), depicting the conditional pmfs for x = 1 and 2.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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
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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