Answered: Example 4-14 The joint density function…

Example 4-14 The joint density function of two continuous random variables X and Y' is expressed below. For c= 0.7426, compute P(X2-0.5, Y ≤2.5). r + 121

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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Question

Example 4-14 The joint density function of two continuous random variables X and Y is
expressed below. For c = 0.7426, compute P(X2 -0.5, Y ≤2.5).
f(x, y) =
x + y
y-1
for 1≤x≤0 and 2≤ y ≤ 3,
-
otherwise.

Expert Solution

Step 1: Write the given information:

From the given information, the joint density function for X and Y is,

$f open parentheses x comma y close parentheses equals c fraction numerator x plus y over denominator y minus 1 end fraction comma space minus 1 less or equal than x less or equal than 0 comma space 2 less or equal than y less or equal than 3$

For c=0.7426.

Therefore,

$f open parentheses x comma y close parentheses equals 0.7426 fraction numerator x plus y over denominator y minus 1 end fraction comma space minus 1 less or equal than x less or equal than 0 comma space 2 less or equal than y less or equal than 3$

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