**Problem 7:** Random variables $ X $ and $ Y $ have joint PDF\[f_{X,Y}(x,y) = \begin{cases} 12e^{-(3x+4y)}, & x \geq 0, y \geq 0, \\0, & \text{otherwise.}\end{cases}\](a) Find $ P[X + Y \leq 1] $.(b) Find $ P[\min(X,Y) \geq 2] $.(c) Find $ P[\max(X,Y) \leq 0.5] $.

Introduction: The joint density function of two random variables X and Y is given below: (a). Find…

Answered: Problem 7: Random variables X and Y…

Problem 7: Random variables X and Y have joint PDF 12e-(kr+), r 2 0, y 2 0, Sx.x (2, y) { 0, otherwise. (a) Find P(X +Y s 1).

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

**Problem 7:** Random variables $ X $ and $ Y $ have joint PDF

\[
f_{X,Y}(x,y) =
\begin{cases}
12e^{-(3x+4y)}, & x \geq 0, y \geq 0, \\
0, & \text{otherwise.}
\end{cases}
\]

(a) Find $ P[X + Y \leq 1] $.

(b) Find $ P[\min(X,Y) \geq 2] $.

(c) Find $ P[\max(X,Y) \leq 0.5] $.

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