Please solve (a) & (b) only! The two-parameter gamma distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in (4.8),x 2 0f(x; a) =r(a)(4.7)otherwiseby x - y and x 2 0 by x 2 y. This amounts to shifting the density curves in the figure below so that they begin their ascent or descent at y rather than 0.f(x; a, ß) 4f(x; a,)a = 2, B =1.0 –1.0 -a = 1a = 1, B = 10.5 -a = .6a = 2, B = 20.5 -a = 2a = 5a = 2, B = 1137(a) gamma density curves(b) standard gamma density curvesA study employs this distribution to model x = 3-day flood volume (10° m). Suppose that values of the parameters are a = 12, B = 8, y = 44 (very close to estimates in the cited article based on past data).(a) What are the mean value and standard deviation of X? (Round your answers to four decimal places.)10°m3meanstandard deviation| 10°m3(b) What is the probability that flood volume is between 100 and 151? (Round your answer to three decimal places.)(c) What is the probability that flood volume exceeds its mean value by more than one standard deviation? (Round your answer to three decimal places.)(d) What is the 95th percentile of the flood volume distribution? (Round your answer to two decimal places.)10°m3

here we have given ,let the random variable X represents the flood volume . here random variable X…

The two-parameter gamma distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in (4.8), x 20 f(x; a) = r(a) (4.7) otherwise by x – y and x 2 0 by x 2 y. This amounts to shifting the density curves in the figure below so that they begin their ascent or descent at y rather than o. f(x; a, ß) 4 1.0- f(x; a.) + a = 2, ß = { 1.0 - a = 1 , a = 1, ß = 1 0.5- ‚a = .6 ,a = 2, ß = 2 0.5 - a = 2 ‚a = 5 a = 2, ß = 1 5 6 7 4

The two-parameter gamma distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in (4.8), x 20 f(x; a) = r(a) (4.7) otherwise by x – y and x 2 0 by x 2 y. This amounts to shifting the density curves in the figure below so that they begin their ascent or descent at y rather than o. f(x; a, ß) 4 1.0- f(x; a.) + a = 2, ß = { 1.0 - a = 1 , a = 1, ß = 1 0.5- ‚a = .6 ,a = 2, ß = 2 0.5 - a = 2 ‚a = 5 a = 2, ß = 1 5 6 7 4

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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