Consider the accompanying observations on stream flow (1000s of acre-feet) recorded at a...

Consider the accompanying observations on stream flow (1000s of acre-feet) recorded at a station in Colorado for the period April 1–August 31 over a 31-year span (from an article in the 1974 volume of Water Resources Research).

An appropriate probability plot supports the use of the lognormal distribution (see Section 4.5) as a reasonable model for stream flow.

a. Estimate the parameters of the distribution. [Hint: Remember that X has a lognormal distribution with parameters μ and σ² if ln(X) is normally distributed with mean μ and variance σ².]

b. Use the estimates of part (a) to calculate an estimate of the expected value of stream flow. [Hint: What is E(X)?]