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Math Help - Normal Distribution

  1. #1
    Senior Member Dinkydoe's Avatar
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    Normal Distribution

    Given that X,Y are independant Normal distributed variables, with N(1,\sigma^2), \sigma = \frac{1}{2}

    How do I calculate P(X+Y\leq t)


    I'm not quite sure how to calculate this since the cdf of the normal distribution doesn't have a closed form. And approximating with an error-function seems quite a bother. Any hints?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Let Z=X+Y, then Z\sim N(E(Z), V(Z))

    you want P(Z\le t)=\int_{-\infty}^t f_Z(z)dz
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