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. 1/100 (b) Find P(X ≤ 0.75, Y≤ 1.25). (Round answer to five decimal places). 0.054075 X (c) Find P(X ≤ 0.75, Y≤ 1.25, Z ≤ 1). (Round answer to six decimal places). 0.005146 X
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. 1/100 (b) Find P(X ≤ 0.75, Y≤ 1.25). (Round answer to five decimal places). 0.054075 X (c) Find P(X ≤ 0.75, Y≤ 1.25, Z ≤ 1). (Round answer to six decimal places). 0.005146 X
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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![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.
1/100
(b) Find P(X ≤ 0.75, Y≤ 1.25). (Round answer to five decimal places).
0.054075
(c) Find P(X ≤ 0.75, Y≤ 1.25, Z≤ 1). (Round answer to six decimal places).
0.005146](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b96ff29-61c4-4a18-af2c-3972ac9128c6%2F2c0bdb04-10c4-4b92-a4b3-ff6047ee2ae3%2Fik0j3k_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
1/100
(b) Find P(X ≤ 0.75, Y≤ 1.25). (Round answer to five decimal places).
0.054075
(c) Find P(X ≤ 0.75, Y≤ 1.25, Z≤ 1). (Round answer to six decimal places).
0.005146
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