For a random variable X (which is > 0), if logX ~ N(mu, sigma^2), we call the distribution of X "log normal distribution" and write it as X ~ Lognormal(mu, sigma^2) . Show the following: When X ~...

For a random variable X (which is > 0), if logX ~ N(mu, sigma^2), we call the distribution of X "log normal distribution" and write it as X ~ Lognormal(mu, sigma^2) . Show the following: When X ~ Lognoraml(0, 1), the moment generating function of X does not exist.