Suppose that Y has density function f (y) = $ ky(1 y), 0 y 1, 0, elsewhere. a Find the

Chapter 4, Problem 4.8

(choose chapter or problem)

Suppose that Y has density function

\(f(y)=\left\{\begin{array}{ll}
k y(1-y), & 0 \leq y \leq 1 \\
0, & \text { elsewhere }
\end{array}\right.\)

a Find the value of k that makes f(y) a probability density function.

b Find \(P(.4 \leq Y \leq 1)\).

c Find \(P(.4 \leq Y<1)\).

d Find \(P(Y \leq .4 \mid Y \leq .8)\).

e Find \(P(Y<.4 \mid Y<.8)\).