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.
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.
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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Question
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.
? =
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