Unformatted text preview: Î» + Î¼ . Note that it is not always the case that the sum of two independent random variables will be a random variable of the same type. If X and Y are independent normals, thenY is also a normal (with E (Y ) =E Y and Var (Y ) = (1) 2 Var Y = Var Y ), and so XY is also normal. To deï¬ne a conditional density in the discrete case, we write p X  Y = y ( x  y ) = P ( X = x  Y = y ) . This is equal to P ( X = x,Y = y ) P ( Y = y ) = p ( x,y ) p Y ( y ) . Analogously, we deï¬ne in the continuous case f X  Y = y ( x  y ) = f ( x,y ) f Y ( y ) . 37...
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 Spring '10
 ansan
 Probability theory, Nonnegative integer values

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