Q5. A continuous r.v. X is said to have a Gamma (a, B) distribution if its moment generating function (m.g.f.) is given by M x (1) = (1- ßt). Let X1,X 2,.,X , be a random sample of size n from an exponential distribution with mean 1/0 and m.g.f. (1-0t). Let Y =EX; i =l 1 Ex (For p.d.f.s of Gamma and Exponential, and X i =1 (a) Find the m.g.f. My (t) of Y and state the distribution of Y specifying the parameters. (b) Find the m.g.f. M (t) of X and state the distribution of X specifying the parameters. (c) Suppose you have a random sample of size n = 100 from a Gamma (a, B) distribution with a = 3 and B = 5/3. Use the Central Limit Theorem to find P(4.5

Q5. A continuous r.v. X is said to have a Gamma (a, B) distribution if its moment generating function (m.g.f.) is given by M x (1) = (1- ßt). Let X1,X 2,.,X , be a random sample of size n from an exponential distribution with mean 1/0 and m.g.f. (1-0t). Let Y =EX; i =l 1 Ex (For p.d.f.s of Gamma and Exponential, and X i =1 (a) Find the m.g.f. My (t) of Y and state the distribution of Y specifying the parameters. (b) Find the m.g.f. M (t) of X and state the distribution of X specifying the parameters. (c) Suppose you have a random sample of size n = 100 from a Gamma (a, B) distribution with a = 3 and B = 5/3. Use the Central Limit Theorem to find P(4.5

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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