(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X represent the random choice of a real number on the interval [-1,1] which has a uniform distribution such that the probability density function is[tex]f_{X}(x)=\frac{1}{2}[/tex] when [tex]-1\leqx\leq1[/tex]. Let[tex] Y=X^{2}[/tex] a. Find the cumulative distribution [tex]F_{Y}(y)[/tex] b. the density function [tex]f_{Y}(y)[/tex] and c. the expected value [tex]E(Y)[/tex].

2. Relevant equations

my book gives a great explanation on how to change variables for joint distributions, but little is said about functions of one random variable, so I'm kind of at a loss here.

3. The attempt at a solution

first, if [tex]Y=X^{2}[/tex], then I want to say we need to find Y over the interval

[0,1]. And integrating I have that:

[tex]F_{X}(x)=\frac{x+1}{2}[/tex] which is [tex]P(X\leqx)[/tex]...

now I want to say [tex]P(X\leqx)=P(\sqrt{Y}\leqx)[/tex]...

i'm not sure where to go from here...

can I just substitute [tex] \sqrt{y} [/tex] for x so I have:

[tex]F_{Y}(y)=\frac{\sqrt{y}+1}{2}[/tex] ??

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# Homework Help: Find cdf, pdf and expextation value of a random variable

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