6. 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).

127.96 210.07 203.24 108.91 178.21 285.37 100.85 89.59 185.36 126.94 200.19 66.24 247.11 299.87 109.64 125.86 114.79 109.11 330.33 85.54 117.64 302.74 280.55 145.11 95.36 204.91 311.13 150.58 262.09 477.08 94.33 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 and 2 if ln(X) is normally distributed with mean and variance 2

.]

b. Use the estimates of part

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