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Thread: bivariate normal distribution

  1. #1
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    bivariate normal distribution

    if $\displaystyle X,Y \sim BVN $ AND : $\displaystyle \mu \scriptscriptstyle {x} =-3$ $\displaystyle \sigma \scriptscriptstyle {x} =5$ $\displaystyle \mu \scriptscriptstyle {y} =10$ $\displaystyle \sigma \scriptscriptstyle {y} = 3$ $\displaystyle \rho =\frac{3}{5}$ how i can find : $\displaystyle p(-5\prec x \prec 5) $ ???????
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    Hello,
    Quote Originally Posted by flower3 View Post
    if $\displaystyle X,Y \sim BVN $ AND : $\displaystyle \mu \scriptscriptstyle {x} =-3$ $\displaystyle \sigma \scriptscriptstyle {x} =5$ $\displaystyle \mu \scriptscriptstyle {y} =10$ $\displaystyle \sigma \scriptscriptstyle {y} = 3$ $\displaystyle \rho =\frac{3}{5}$ how i can find : $\displaystyle p(-5\prec x \prec 5) $ ???????
    If (X,Y) follows a bivariate normal distribution, then in particular, X follows a normal distribution.
    Its mean is -3 and its variance is 5^2=25.
    Now, can you answer your own question ?

    Spoiler:
    $\displaystyle X\sim\mathcal{N}(-3,25)$

    --> $\displaystyle \frac{X+3}{5}\sim\mathcal{N}(0,1)$

    $\displaystyle \mathbb{P}(-5<X<5)=\mathbb{P}\left(\frac{-5+3}{5}<\frac{X+3}{5}<\frac{5+3}{5}\right)$
    then use a z-table
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