A random variable Y has probability density function given by for y > 0. a. Demonstrate that

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A random variable Y has probability density function given by1 1 hy(y) = = /2/7/7 exp (-/12 (1m y5) 12 Y (In -

for y > 0.

a. Demonstrate that hY(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.

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