Q.1 1. Let X have the probability density function f(x) = cr(1-x) for 0≤x≤ 1 and f(x) = 0 otherwise.(a) Show that c = 6.(b) Find the cumulative distribution function F(x) = P(X ≤r).(c) Calculate P(.1 < X < .5).(d) Find the mean, variance and standard deviation of X.

The probability density function of random variable X is given as:

Answered: 1. Let X have the probability density…

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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1. Let X have the probability density function f(x) = cr(1-r) for 0≤x≤1 and f(x) = 0 otherwise. (a) Show that c = 6. (b) Find the cumulative distribution function F(x) = P(X ≤ r). (c) Calculate P(.1 < X <.5). (d) Find the mean, variance and standard deviation of X.