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sys 3, and f(x, y) = 0 elsewhere. e of A? = 2, 1 = Y = 2)? rginal probability density functions f(x) and fy(y). variables X and Yindependent? the conditional probability density function of X?

sys 3, and f(x, y) = 0 elsewhere. e of A? = 2, 1 = Y = 2)? rginal probability density functions f(x) and fy(y). variables X and Yindependent? the conditional probability density function of X?

A First Course in Probability (10th Edition)
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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2.5.5Suppose that two continuous random variables X and Yhave a joint probability density function f(x, y) = A(exy + ²xy) for 1 ≤ x ≤ 2 and 0 ≤ y ≤ 3, and f(x, y) = 0 elsewhere. (a) What is the value of A? (b) What is P(1.5 = X = 2, 1 = Y = 2)? (c) Construct the marginal probability density functions f(x) and fy(y). (d) Are the random variables X and Yindependent? (e) If Y= 0, what is the conditional probability density function of X?
Transcribed Image Text:2.5.5Suppose that two continuous random variables X and Yhave a joint probability density function f(x, y) = A(exy + ²xy) for 1 ≤ x ≤ 2 and 0 ≤ y ≤ 3, and f(x, y) = 0 elsewhere. (a) What is the value of A? (b) What is P(1.5 = X = 2, 1 = Y = 2)? (c) Construct the marginal probability density functions f(x) and fy(y). (d) Are the random variables X and Yindependent? (e) If Y= 0, what is the conditional probability density function of X?
Expert Solution
Step 1

For the continuous random variables the joint probability density function is a function satisfying,

The probability that  and  is obtained from the joint probability density function as,

 

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