fxy(y1y2) = 7e-(2y1+3y2) ; y1,y2 > 0 1. Verify that this is properly normalized. 2. Are...

Question

Question

f_xy(y₁y₂) = 7e^{-(2y₁+3y₂)} ; y_1,y₂ > 0

1. Verify that this is properly normalized.

2. Are Y1 and Y2 independent?

Answer 1

Answer #1

1)

It should be 6 instead of 7

y1 = x, y2 = y

$int _0^{infty :}int _0^{infty :}6e^{-left(2x+3y ight)}dxdy=1$

$Зу$

$int _0^{infty :}3e^{-3y}dy=1$

2)

Yes ,

f(y2) = 3 e^(-3y2)

f(y1) = 2 e^ (-2y1)

As

f(y1, y2) = f(y1) f(y2)

Y1 and Y2 are independent

Answer 2

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