2. (a) Suppose that a random variable X has a moment generating function given byMx(t) = 31 21Find E[X] and V[X).(b) Now suppose that X1, X2,... , Xn.. are i.i.d. copies of the random variable X from part (a),and define the random variables.S, = X1 + Xạ + c ..+ Xp.Find expressions for the numbers a, and b, so thatSn - an+ Z as n+0o,where Z- N(0, 1).

Part a]: Provided information is ; Random variable x has moment generating function is given by ;…

2. (a) Suppose that a random variable X has a moment generating function given by 1 1 Mx(t) =+e + Find E[X] and V[X]. (b) Now suppose that X1, X2,..X are ii.d. copies of the random variable X from part (a), and define the random variables. S, = X1 + Xạ +c..+ Xp. Find expressions for the mumbers a, and b, so that S. - an → Z as n→ 0, b where Z- N(0, 1).

2. (a) Suppose that a random variable X has a moment generating function given by 1 1 Mx(t) =+e + Find E[X] and V[X]. (b) Now suppose that X1, X2,..X are ii.d. copies of the random variable X from part (a), and define the random variables. S, = X1 + Xạ +c..+ Xp. Find expressions for the mumbers a, and b, so that S. - an → Z as n→ 0, b where Z- N(0, 1).

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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