6. Consider the accompanying observations on stream ow (1000 s 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 Res.).

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 ow.

a. Estimate the parameters of the distribution.
[Hint: Remember that X has a lognormal distribution with parameters m and s2 if ln(X) is normally distributed with mean m and variance s2.]

b. Use the estimates of part

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