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Math Help - Continuous Random Variable and Density Function

  1. #1
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    Continuous Random Variable and Density Function

    Let X be a continuous random variable with density function f(x)=.5e^-abs(x) for x in all real numbers. Find EX and var(y)

    I got 0 for both values and im not sure if i did this right.... Can anyone help?

    Thanks!!!
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by clipperdude21 View Post
    Let X be a continuous random variable with density function f(x)=.5e^-abs(x) for x in all real numbers. Find EX and var(y)

    I got 0 for both values and im not sure if i did this right.... Can anyone help?

    Thanks!!!
    f(x) = \frac{1}{2}e^{-|x|}
    so,
    E[X] = \int_R xf(x)dx = \int_{-\infty}^0 \frac{1}{2}xe^{x}dx + \int_{0}^{\infty} \frac{1}{2}xe^{-x}dx

    if this is what you did, probably you are right..
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  3. #3
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    thats what i set it up as but somehow im second guessing my calculus i integrated it and got .5E^x(x-1) and -.5e^-x(x+1) for the other and i didnt know if i did that right...
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by clipperdude21 View Post
    thats what i set it up as but somehow im second guessing my calculus i integrated it and got .5E^x(x-1) and -.5e^-x(x+1) for the other and i didnt know if i did that right...
    can you show your complete solution?
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  5. #5
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    If that is what you did it does integrate to 0, but is wrong, you should have had:

    E[X] = \int_R xf(x)dx = \int_{-\infty}^0 \frac{1}{2}xe^{-x}dx + \int_{0}^{\infty} \frac{1}{2}xe^{-x}dx

    which does not integrate up to 0.

    RonL
    notice that there is an absolute value sign there and by definition,
     |x| = \left\{ {\begin{array}{cc}<br />
x&x \geq 0\\<br />
-x&x < 0\\<br />
\end{array}}\right.<br />

    or i just had a wrong interpretation?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by kalagota View Post
    notice that there is an absolute value sign there and by definition,
     |x| = \left\{ {\begin{array}{cc}<br />
x&x \geq 0\\<br />
-x&x < 0\\<br />
\end{array}}\right.<br />

    or i just had a wrong interpretation?
    No ignore my post I had misread the integrals

    RonL
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  7. #7
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    No ignore my post I had misread the integrals

    RonL
    ok..
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