Ecologists are studying the lives of teporingos arriving at a den. Let X be the number of minutes a teporingo spends at the den, and Y be the number of minutes spent in sleeping at the den. It is known that 1 fx,y(x, y) = -x/0 e-x/0 02 on 0 < Y≤ X < ∞. Find an expression to compute P[2Y > X]. -x/0 SoSe / dydx /2 02 2y 1 -x/dxdy 02 e Szy So 1 02 -x/dxdy S2 So 2 1 Xex/dxdy 02 -x/dxdy Joe/dady

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Ecologists are studying the lives of teporingos arriving at a den. Let X be the
number of minutes a teporingo spends at the den, and Y be the number of minutes
spent in sleeping at the den. It is known that
1
fx,y(x, y) =
-x/0
e-x/0
02
on 0 < Y≤ X < ∞.
Find an expression to compute P[2Y > X].
-x/0
SoSe / dydx
/2 02
2y 1 -x/dxdy
02
e
Szy So
1
02
-x/dxdy
S2 So
2
1
Xex/dxdy
02
-x/dxdy
Joe/dady
Transcribed Image Text:Ecologists are studying the lives of teporingos arriving at a den. Let X be the number of minutes a teporingo spends at the den, and Y be the number of minutes spent in sleeping at the den. It is known that 1 fx,y(x, y) = -x/0 e-x/0 02 on 0 < Y≤ X < ∞. Find an expression to compute P[2Y > X]. -x/0 SoSe / dydx /2 02 2y 1 -x/dxdy 02 e Szy So 1 02 -x/dxdy S2 So 2 1 Xex/dxdy 02 -x/dxdy Joe/dady
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