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Probabilities with Joint Distribution

Using the joint distribution for two RVs X and Y given by F_XY(x,y) = u(x)u(y)[l-e^(-ax)-e^(-ay)+e^(-a(x+y))] and assuming a = 0.5 in each case, find the probabilities:

a) P {X </= 1, y </= 2}
B) P {0.5 < X < 1.5}
C) P {-1.5 < X </= 2, 1 < Y /= 3}

Solution Preview

a) P (X ≤ 1; Y ≤ 2) = F (1,2) = 1 - e^-1/2 -e ^-1/2*2 + e ^ -1/2 (1+2)
= 1 - e^ -1/2 - e + -3/2 = 0.24872

b) P (0.5 ...

Solution Summary

Calculations alone are shown to find the probabilities in a case of joint distribution for a=0.5.

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