The random variable Y has probability density functionf(V) = k(y + y³),0 < y< 2and zero otherwise, where k is a positive constant.i) Show that k =!ii) Show that the cumulative distribution function isy? (y? + 2)F(y) =120 < y< 22y > 2.Hence find PG < Y <).iii) Find the variance of Y.

Answered: The random variable Y has probability…

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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Question

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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