Let X be a continuous random variable with E(X)=i! for i=0,1,2,.... (a) Show that X has an exponential distribution. State its parameter. (b) If X₁, X₂,..., X₁ are independent observations for X. Calculate the probability that 4 out 10 observations are greater than 5.

Let X be a continuous random variable with E(X)=i! for i=0,1,2,.... (a) Show that X has an exponential distribution. State its parameter. (b) If X₁, X₂,..., X₁ are independent observations for X. Calculate the probability that 4 out 10 observations are greater than 5.

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 42CR

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Question

Let X be a continuous random variable with E(X¹)=i! for i=0,1,2,....
(a)
Show that X has an exponential distribution. State its parameter.
(b)
If X₁, X₂,..., X₁ are independent observations for X. Calculate the probability
10
that 4 out 10 observations are greater than 5.

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