6.E.503 XF of at a station in for the period April 1-August 31 over a 31-year sp

Question

6.E.503 XF of at a station in for the period April 1-August 31 over a 31-year span. 89.59 280.55 526.14 108.91 262.09 185.36 66.24 150.58 58.30 299.87 97.26 127.96 210.07 311.13 100.85 204.91 20019 302.74 109.11 330.33 247.11 94.33 131.88 198.84 145.1 125.86 114.7947.64285.3717.64 203.24 An appropriate probability plot supports the use of the lognormal distribution as a reasonable model for stream flow. a) Estimate the parameters of the distribution. H C Remember that X has a log orm al distribution with parameters and 2 x is normally distributed with mean and variance o2.1 (Round your estimate for the mean to three decimal places, and round your estimate for the variance to four decimal places. ) (b) use the estimates of part (a) to calculate an estimate of the expected vaiue of stream fow. EHint: what is E(xg7) (Round your answer to two decimal places.) interval for the true average echo duration u. (Round your answers to two decimal places.)

Explanation / Answer

Here the logarithm table

(a) ^ = 5.0710

2 = 0.3090

(b) Here expected value of stream flow E(x) = EXP ( + 2/2) = EXP (5.0710 + 0.3090/2) = 185.9438

x ln(x) 89.59 4.4952 280.55 5.6368 526.14 6.2656 108.91 4.6905 262.09 5.5687 185.36 5.2223 66.24 4.1933 150.58 5.0145 58.3 4.0656 299.87 5.7033 97.26 4.5774 127.96 4.8517 210.07 5.3474 311.13 5.7402 100.85 4.6136 204.91 5.3226 200.19 5.2993 302.74 5.7129 109.11 4.6924 330.33 5.8001 247.11 5.5098 94.33 4.5468 131.88 4.8819 198.84 5.2925 145.11 4.9775 125.86 4.8352 114.79 4.7431 47.64 3.8637 285.37 5.6538 117.64 4.7676 203.24 5.3144 Mean 5.0710 Variance 0.3090

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