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Math Help - Gaussian random variable with PDF

  1. #1
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    Gaussian random variable with PDF

    Hi, I had a question I am hoping someone can give me some pointers on.

    Question: Guaussian random variable X with PDF, fx(x)=1/(sqrt(2*pi))*e^(-x^2/2) ; -infinity< x < +infinity.

    a) The Gaussian is passed through a square law device with output Y=X^2. Find the PDF of Y.
    b) THe Gaussian is "passed through a full wave rectifier with output Y=absolutevalue(X). Find the PDF of Y
    *See attached image for hint given

    Second part to question: Consider the three level limiter shown in the figure (attached)

    a)Find the PDF of Y if X is the Gaussian PDF of the previous problem. Express answer in terms of the CDF of X given by phi(x)=integral from t=-infinity to t=x of 1/(sqrt(2*pi))*e^(-t^2/2) dt
    b)Sketch both the PDF , fY(y) and the CDF, FY(y) for the random variable Y.
    Thanks for whatever help I can get!
    Attached Thumbnails Attached Thumbnails Gaussian random variable with PDF-img02.jpg   Gaussian random variable with PDF-img01.jpg  
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  2. #2
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    Quote Originally Posted by Bob001 View Post
    Hi, I had a question I am hoping someone can give me some pointers on.

    Question: Guaussian random variable X with PDF, fx(x)=1/(sqrt(2*pi))*e^(-x^2/2) ; -infinity< x < +infinity.

    a) The Gaussian is passed through a square law device with output Y=X^2. Find the PDF of Y.
    [snip]
    Read this: http://www.mathhelpforum.com/math-he...tml#post119542
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  3. #3
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    Quote Originally Posted by Bob001 View Post
    Hi, I had a question I am hoping someone can give me some pointers on.

    Question: Guaussian random variable X with PDF, fx(x)=1/(sqrt(2*pi))*e^(-x^2/2) ; -infinity< x < +infinity.

    [snip]

    b) THe Gaussian is "passed through a full wave rectifier with output Y=absolutevalue(X). Find the PDF of Y
    *See attached image for hint given

    [snip]
    Use the same technique as (a). Here's a start:

    The cdf of Y is F(y) = \Pr(Y < y) = \Pr(|X| < y) = \Pr(-y < X < y) = 2 \Pr(0 < X < y).

    Now get into the calculation.
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  4. #4
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    Nice work Mr. Fantastic.
    For the first part X^2 should be standard Chi-square distibution. Should not be hard to drive its pdf algebrically.

    -O
    Last edited by mr fantastic; February 7th 2009 at 08:01 PM. Reason: Removed link not relevant to question (looks like a signature but isn't)
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  5. #5
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    Thank you for the tips!
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