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Thread: Math Stats and Probability proof help

  1. #1
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    Math Stats and Probability proof help

    Let X ~ Unif(0,1) and Y ~ Unif(0,1) be independent. Let Z = X +Y. Find the pdf for Z and use this to show that Z is NOT Unif(0,2). Thus the sum of two independent uniform random variables is not itself a uniform random variable.

    Is this the correct answer?

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  2. #2
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    Re: Math Stats and Probability proof help

    density function is correct,

    expectation is not,

    check your math.
    Thanks from ballerninja29
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    Re: Math Stats and Probability proof help

    Does E(x)= (a+b)/2, so then would it be (0+2)/2?
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    Re: Math Stats and Probability proof help

    Quote Originally Posted by ballerninja29 View Post
    Does E(x)= (a+b)/2, so then would it be (0+2)/2?
    $\displaystyle E[X] = \int_{-\infty}^{\infty}~x f_X(x)~dx = \int_0^1~x^2~dx + \int_1^2 x(2-x)~dx$

    $E[X] = \left . \dfrac{x^3}{3}\right|_0^1 + \left . x^2-\dfrac{x^3}{3}\right|_1^2= \dfrac 1 3 + 4 - \dfrac 8 3 - 1 + \dfrac 1 3 = \dfrac 1 3 + \dfrac 2 3 = 1$
    Last edited by romsek; Apr 16th 2017 at 07:44 PM.
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    Re: Math Stats and Probability proof help

    Quote Originally Posted by ballerninja29 View Post
    Let X ~ Unif(0,1) and Y ~ Unif(0,1) be independent. Let Z = X +Y. Find the pdf for Z and use this to show that Z is NOT Unif(0,2). Thus the sum of two independent uniform random variables is not itself a uniform random variable. Is this the correct answer?
    If you want help why do you not post readable questions?
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