Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) 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 ≤ 0.875 , Y ≤ 1.125). (Round answer to five decimal places). (c) Find P(X ≤ 0.875 , Y ≤ 1.125 , Z ≤ 1). (Round answer to six decimal places).

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) 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 ≤ 0.875 , Y ≤ 1.125). (Round answer to five decimal places). (c) Find P(X ≤ 0.875 , Y ≤ 1.125 , Z ≤ 1). (Round answer to six decimal places).

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

Suppose X, Y, and Z are random variables with the joint density function

f(x, y, z) = Ce^{−(0.5x + 0.2y + 0.1z)} 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 ≤ 0.875 , Y ≤ 1.125). (Round answer to five decimal places).

(c) Find P(X ≤ 0.875 , Y ≤ 1.125 , Z ≤ 1). (Round answer to six decimal places).

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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