4. (i) Let a be a positive constant andf(x) = ax² e −4xx = R.Find a such that f(x) is a probability density function.[6 Marks](ii) Let X be a random variable with probability density function in (i)(a) Find (A), the characteristic function of the random variable X.(b) Using (A), calculate E(X) and Var(X).[15 Marks][14 Marks]

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Answered: 4. (i) Let a be a positive constant and…

A First Course in Probability (10th Edition)

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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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