**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) $.

The probability function will give 1 for:∫z=0∞∫y=0∞∫x=0∞fx,y,zdxdydz. Solving and finding value of…

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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Question

**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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