Let X be a continuous random variables with with the following probability density function. Answer the following questions. Find the value of α such that f(x) is a probability density function. Make sure that you show all the steps.

A First Course in Probability (10th Edition)

10th Edition

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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Question

Let X be a continuous random variables with with the following probability density function.
Answer the following questions.
Find the value of α such that f(x) is a probability density function. Make sure that
you show all the steps.
Find the cumulative distribution function of X. Show it on a graph. Make sure that
you show all the steps.
Find the expected value and variance of X. Make sure that you show all the steps.
Find the probability density function of Y = X2. Make sure that you show all the
steps.

Let X be a continuous random variables with with the following probability density function.
{
f(x) =
0
steps.
X
+x²
0 < x <a
otherwise
Answer the following questions.
Find the value of a such that f(x) is a probability density function. Make sure that
you show all the steps.
Find the cumulative distribution function of X. Show it on a graph. Make sure that
you show all the steps.
Find the expected value and variance of X. Make sure that you show all the steps.
Find the probability density function of Y X². Make sure that you show all the

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