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. 1/100 (b) Find P(X ? 1 , Y ? 1.25). (Round answer to five decimal places). (c) Find P(X ? 1 , Y ? 1.25 , 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.
1/100
(b) Find P(X ? 1 , Y ? 1.25). (Round answer to five decimal places).
(c) Find P(X ? 1 , Y ? 1.25 , 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.
1/100
(b) Find P(X ? 1 , Y ? 1.25). (Round answer to five decimal places).
(c) Find P(X ? 1 , Y ? 1.25 , Z ? 1). (Round answer to six decimal places).

Added by Susan R.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Hoan Nguyen

06/01/2023

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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 ≤ 1 , Y ≤ 1.25). (Round answer to five decimal places). (c) Find P(X ≤ 1 , Y ≤ 1.25 , Z ≤ 1). (Round answer to six decimal places).