50. Suppose X, Y, and Z are random variables with joint density function f(x, y, z) = Ce-@5«+02y+012} if x > 0, y > 0, z > 0, and f(x, y, z) = 0 otherwise. (a) Find the value of the constant C. (b) Find P(X < 1, Y< 1).
50. Suppose X, Y, and Z are random variables with joint density function f(x, y, z) = Ce-@5«+02y+012} if x > 0, y > 0, z > 0, and f(x, y, z) = 0 otherwise. (a) Find the value of the constant C. (b) Find P(X < 1, Y< 1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 50:**
Suppose \( X, Y, \) and \( Z \) are random variables with joint density function
\[ f(x, y, z) = Ce^{-(0.5x + 0.2y + 0.1z)} \]
if \( x \geq 0, y \geq 0, z \geq 0 \), and
\[ f(x, y, z) = 0 \]
otherwise.
**(a)** Find the value of the constant \( C \).
**(b)** Find \( P(X \leq 1, Y \leq 1) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3f07c85-763f-4eec-8c61-50ee452049fe%2F5399af4a-d8a7-49ef-b999-a41e49c99f08%2F2s6dx2_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 50:**
Suppose \( X, Y, \) and \( Z \) are random variables with joint density function
\[ f(x, y, z) = Ce^{-(0.5x + 0.2y + 0.1z)} \]
if \( x \geq 0, y \geq 0, z \geq 0 \), and
\[ f(x, y, z) = 0 \]
otherwise.
**(a)** Find the value of the constant \( C \).
**(b)** Find \( P(X \leq 1, Y \leq 1) \).
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