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Math Help - Subtracting two normal distributions

  1. #1
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    Subtracting two normal distributions

    I have two distributions X~N(.65,.0002) and Y~N(.59,.0003) if I want the mean and SD do I just subtract them? and is X-Y also a normal distribution?
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    Hello,

    If they're independent, X-Y will indeed be a normal distribution.

    Now some properties... :
    \mathbb{E}[aX+bY]=a\mathbb{E}[X]+b\mathbb{E}[Y]

    Var(aX+bY)=a^2Var(X)+b^2Var(Y) if they're independent. If not, you'll have to introduce the covariance (check your lessons)

    So Var(X-Y)=Var(X)+Var(Y), if they're independent. Note that the variance is always positive !
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    Yes X and Y are independent. So would it just be u_{x-y} = .06 and SD_{x-y} = |.0002-.0003|? To add more information to this, X is the diameter of a metal pipe and the Y is the diameter of a pipe clamp so the X must fit inside Y. I'm also trying to figure out the probability that the pipe will fit inside the clamp.
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