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Math Help - Chi-squared distribution and pdf

  1. #1
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    Chi-squared distribution and pdf

    Chi-squared distribution and pdf

    Hi guys, i'm doing this practical on R at the moment based on stochastic calculus, and I'm running a few simulations on some sample data. I have a random variable X~N(0,1). Now during some point in the stochastic calculus i have this random variable (X^2)/2 - 1/2. Now since X is normally distributed, I know (X^2)/2 - 1/2 has a chi-squared distribution with degree of freedom one (since we only have one independent random variable). Using R i have produced a histogram of its pdf which i have attached to this post.

    Could anybody give me a formal explanation of why the frequencies of x < 0 is not zero? I thought being chi-squared the values would have all been zero for x < 0? is this because of the constant -1/2 ?

    Please any help would be appreciated, I apologize if the way i've put the question doesnt make sense and please just ask if theres any confusion.

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by euler786 View Post
    Chi-squared distribution and pdf

    Hi guys, i'm doing this practical on R at the moment based on stochastic calculus, and I'm running a few simulations on some sample data. I have a random variable X~N(0,1). Now during some point in the stochastic calculus i have this random variable (X^2)/2 - 1/2. Now since X is normally distributed, I know (X^2)/2 - 1/2 has a chi-squared distribution with degree of freedom one (since we only have one independent random variable). Using R i have produced a histogram of its pdf which i have attached to this post.

    Could anybody give me a formal explanation of why the frequencies of x < 0 is not zero? I thought being chi-squared the values would have all been zero for x < 0? is this because of the constant -1/2 ?

    Please any help would be appreciated, I apologize if the way i've put the question doesnt make sense and please just ask if theres any confusion.

    Thanks
    X^2/2 is intrinsicaly positive (and has a chi-sq distribution with 1 degree of freedom), but you have subtracted 1/2 from this so now it can be negative.

    RonL
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