A random variable Y has probability density function given by

for y > 0.

a. Demonstrate that h_Y(y) is a valid probability density function.

b. Calculate P(1

c. Given that this distribution is actually Log-normal, that is lnY ∼ N(0, 1), use published statistical tables to verify your answer to part b.

You are given that Φ(1.39) = 0.91774 and Φ(0) = 0.5.

1 1 hy(y) = = /2/7/7 exp ( - 1 (1 y5) 12 Y (In -