b) Suppose that a continuous random variable X is associated with the following function:(i) Show that c ==1/15271 Page0 < x < 2,Scx,f(x) = {0, elsewhere.lo,(ii) Calculate the mean and variance of X.(iii) Find the CDF of the random variable X, F(x).(iv) Use either the probability distribution function (pdf) of X, f(x), or the cumulative probabdistribution function (cdf) of X, F(x), to compute P(0.25 < x < 1.25).

As per policy I have calculated first 3 subparts plz REPOST for remaining parts with note I need…

Answered: (i) Show that c = 2 (ii) Calculate the…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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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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(i) Show that c = 2 (ii) Calculate the mean and variance of X. (iii) Find the CDF of the random variable X, F(x).