(a) E(X₂) (b) E(U) (c) V(U)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 3CR
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Question 10
Suppose X₁ and X2 are two independent random variables, as below:
X₁ with p(x) =
2²e-2
for x > 0, and X2 with p(x): - for x > 0. Where λ is a random
variable that is uniformly distributed over the interval from 0 to 2. Also let U = X₁ X₂ . Find:
x!
x!
(a) E(X₂)
(b) E(U)
(c) V(U)
Transcribed Image Text:Question 10 Suppose X₁ and X2 are two independent random variables, as below: X₁ with p(x) = 2²e-2 for x > 0, and X2 with p(x): - for x > 0. Where λ is a random variable that is uniformly distributed over the interval from 0 to 2. Also let U = X₁ X₂ . Find: x! x! (a) E(X₂) (b) E(U) (c) V(U)
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