(a)(b)Let X have a gamma distribution with parameters a = 2 and 0.Find the mode of X. Recall that the mode of a continuous randomvariable is the value where the pdf is the highest.If the mode is two, find P(X < 9.488). Tables are allowed for thisproblem only if sufficient justification is provided.(c)Find the fifth moment of X without the use of the moment gen-erating function. Simplify completely.

Given that X has gamma distribution with parameters .The PDF of X is given as:

Answered: Let X have a gamma distribution with…

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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Let X have beta distribution with a =2 and B = 3. Then the mean and the variance of X, respectively, are Select one: O a. 0.04 and 04 O b. 0.02 and 0.04 O c. 0.4 and 0.04 O d. 0.4 and 0.20 The weekly downtime Y (in hours) for a certain industrial machine has approximately gamma distribution a =3 and B =2. The loss, in dollars, to the industrial operation as a result of this downtime is given by L = 30Y+2Y?. Find the expected value of L. Select one: O a. 180 O b. 98 Oc. 36 O d. 276 The length X to complete a certain key task in house construction is exponentially distributed with mean of 5 hours. The cost of completing this task is C = 10+20x2, Find the expected cost. Select one: O a. 1000 O b. 1010 O c. 510 O d. 500 sum of the dead load plus the The total sustained load on the concrete footing of a planned building is occupancy load. Suppose that the dead load X, has a gamma distribution with a = 10 and B= 30, whereas the occupancy load, X2 also has exponential distribution with e =…
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Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.
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Let X have a gamma distribution with parameters a = 2 and 0. Find the mode of X. Recall that the mode of a continuous random variable is the value where the pdf is the highest.