A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
Follow the example. Answer the exercise 4
Example 14. Suppose fx,y (x, y) = (x + y)I(0,1) (2) I(0,1) (y). From Example 12 we got fx(z) = (2 + 1 ) 4 (0,1)(2). Thus we have x+y fy|x (y|x) (x+y)I(0,1)(x) I(0,1) (y) (x + ¹) (0,1)(x) I(0,1) (y) x+ for 0<x< 1. Note that Fyx (yr) = fy\x (2/2) dz x+z 1 dz= = J₁ x + 1 Sº (x + 2) dz x+ // Jo 1 +++ (²0+1²) for 0 < y < 1. x+ Exercise 4. Let X and Y be jointly continuous random variables with joint PDF given by : 1 fx.y(2,y)= = x(1 +3y²) I(0,2)(x) I(0,1) (y). a. Find the conditional PDF of X given Y. b. Find P (< X < / | Y = }). 23 2.2. INDEPENDENCE OF RANDOM VARIABLES pjbaranas c. Find the marginal PDF of X. fxy(2,3) fx(x)
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Transcribed Image Text:Example 14. Suppose fx,y (x, y) = (x + y)I(0,1) (2) I(0,1) (y). From Example 12 we got fx(z) = (2 + 1 ) 4 (0,1)(2). Thus we have x+y fy|x (y|x) (x+y)I(0,1)(x) I(0,1) (y) (x + ¹) (0,1)(x) I(0,1) (y) x+ for 0<x< 1. Note that Fyx (yr) = fy\x (2/2) dz x+z 1 dz= = J₁ x + 1 Sº (x + 2) dz x+ // Jo 1 +++ (²0+1²) for 0 < y < 1. x+ Exercise 4. Let X and Y be jointly continuous random variables with joint PDF given by : 1 fx.y(2,y)= = x(1 +3y²) I(0,2)(x) I(0,1) (y). a. Find the conditional PDF of X given Y. b. Find P (< X < / | Y = }). 23 2.2. INDEPENDENCE OF RANDOM VARIABLES pjbaranas c. Find the marginal PDF of X. fxy(2,3) fx(x)
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