Question

The expected value of Y=e^x
where X∼N(μ,σ)

Answer 1

Step-by-step explanation:The expected value of a function of a random variable is given by the integral of the function times the probability density function of the random variable.

For a normal distribution, the probability density function is given by:

So, the expected value of is given by:

Substituting and into the equation gives:

This integral is not straightforward to solve, but it is a known result that the expected value of an exponential of a normally distributed random variable is:

So, the expected value of where is normally distributed with mean and standard deviation is:

E[Y]=e