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Math Help - pdf and cdf. mean and variance of the pdf

  1. #1
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    pdf and cdf. mean and variance of the pdf

    Hello! there are two problems:

    1) the random variable X has the following pdf : 1/4 if 0<x<4, and 0 otherwise.
    determine the pdf and cdf for the random variable Y=X^1/2.
    what is the expected value of Y?
    what is the variance of Y?

    2) calculate the mean and the variance of returns if they are modeled according to the following pdf: f(x)=1/4 if -1<x<3 , and otherwise f(x)=0.

    thank you for any advice!
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  2. #2
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    Quote Originally Posted by anna30 View Post
    Hello! there are two problems:

    1) the random variable X has the following pdf : 1/4 if 0<x<4, and 0 otherwise.
    determine the pdf and cdf for the random variable Y=X^1/2.
    what is the expected value of Y?
    what is the variance of Y?

    2) calculate the mean and the variance of returns if they are modeled according to the following pdf: f(x)=1/4 if -1<x<3 , and otherwise f(x)=0.

    thank you for any advice!
    One approach is found here: http://www.mathhelpforum.com/math-he...questions.html

    Note that E(X^n) = \int_{-\infty}^{+\infty} x^n f(x) \, dx and Var(X) = E(X^2) - (E(X))^2. These are things you're meant to know, as well as being able to integrate.

    If you need more help please show all your work and say where you get stuck.
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  3. #3
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    Find the transformation T(y) = \sqrt{x} Its inverse T^{-1}(y) = y^2

    Then
    <br />
f_{Y}(y)=f_{X}(T^{-1}(y))|\frac{dT(y)}{dy}|
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