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Math Help - bivariate normal distribution

  1. #1
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    bivariate normal distribution

    if  X,Y \sim BVN AND :  \mu \scriptscriptstyle {x}      =-3  \sigma \scriptscriptstyle {x}       =5  \mu \scriptscriptstyle {y}     =10  \sigma \scriptscriptstyle {y}     = 3  \rho     =\frac{3}{5} how i can find :  p(-5\prec x \prec 5) ???????
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    Hello,
    Quote Originally Posted by flower3 View Post
    if  X,Y \sim BVN AND :  \mu \scriptscriptstyle {x}      =-3  \sigma \scriptscriptstyle {x}       =5  \mu \scriptscriptstyle {y}     =10  \sigma \scriptscriptstyle {y}     = 3  \rho     =\frac{3}{5} how i can find :  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:
    X\sim\mathcal{N}(-3,25)

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

    \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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