A positive random variable X is called lognormal with parameters and 2 if lnX N(, 2). Let X be a lognormal random variable

A positive random variable X is called lognormal with parameters μ and

σ2 if lnX ∼ N(μ, σ2). Let X be a lognormal random variable with parameters μ and σ2.

(a) For a positive integer r, calculate the rth moment of X.

(b) Use the rth moment of X to find Var(X).

(c) In 1977, a British researcher demonstrated that if X is the loss from a large fire, then lnX is a normal random variable. That is, X is lognormal. Suppose that the expected loss due to fire in the buildings of a certain industry, in thousands of dollars, is 120 with standard deviation 36.What is the probability that the loss from a fire in such an industry is less than $100,000?