Let Y be normally distributed with mean and variance ^2. Let =+(^2/2) Find the maximum likelihood estimate for b.

Let Y be normally distributed with mean μ and variance σ^2.

a. Let   φ=μ+(σ^2/2) Find the maximum likelihood estimate for φ

b.Assume the sample size n is large, obtain an asymptotic 95% condence interval for φ

c.Let X = e^Y and X is distributed as lognormal with mean μx = e^φ . Based on the result in part (b), obtain an asymptotic 95% confidence interval for X.