The random variable Y has probability density function fv) = k(y+ y³), 0 < y< 2 and zero otherwise, where k is a positive constant.
The random variable Y has probability density function fv) = k(y+ y³), 0 < y< 2 and zero otherwise, where k is a positive constant.
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 29CR
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![The random variable Y has probability density function
f(V) = k(y + y³),
0 < y< 2
and zero otherwise, where k is a positive constant.
i) Show that k =!
ii) Show that the cumulative distribution function is
y? (y? + 2)
F(y) =
12
0 < y< 2
2
y > 2.
Hence find PG < Y <).
iii) Find the variance of Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe63f5d20-b31b-4b08-94f8-ed070ebd7c8d%2F2999dc44-8db5-4d1b-950a-6109aabb0585%2F1mh5p3p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The random variable Y has probability density function
f(V) = k(y + y³),
0 < y< 2
and zero otherwise, where k is a positive constant.
i) Show that k =!
ii) Show that the cumulative distribution function is
y? (y? + 2)
F(y) =
12
0 < y< 2
2
y > 2.
Hence find PG < Y <).
iii) Find the variance of Y.
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