Let f(x) = k(3x − x2) if 0 ≤ x ≤ 3 and f(x) = 0 if x < 0 or x > 3.(a)For what value of k is f a probability density function?k = (b)For that value of k, find P(X > 1).P(X > 1) =(c)Find the mean.? = Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3.(a) For what value of k is f a probability density function?(b)(c)For that value of k, find P(X > 1).Find the mean.

Answered: Image /qna-images/answer/1c7c8093-29ca-4b7c-a8b6-fe4cf3aec497.jpg

Answered: Let f(x) = (3x - x²) if 0 ≤ x ≤ 3 and…

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

Section13.1: Continuous Probability Models

Problem 7E

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Let f(x) = (3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3. (a) For what value of k is f a probability density function? (b) For that value of k, find P(X > 1). (c) Find the mean.