Exercise 4. Let X and Y be jointly continuous random variables with joint PDF given by : ƒx,y(x, y) = x(1 + 3y²) I(0,2)(x) 1 (0,1) (3). 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.
Exercise 4. Let X and Y be jointly continuous random variables with joint PDF given by : ƒx,y(x, y) = x(1 + 3y²) I(0,2)(x) 1 (0,1) (3). 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.
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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Follow the example. Answer the exercise 4
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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