httpimgurcomLhrcntESolutiona P x11 x21 015 b Px1 x2 008 0

http://imgur.com/LhrcntE

Solution

a)

P( x1=1, x2=1)= 0.15

b)

P(x1 = x2) = 0.08 + 0.15 + 0.10 + 0.07 = 0.4

c)

A = x1 > 2 + x2 U   x2 > 2 + x1

P[X1 > 2 + X2] = P( x1=0 , x2= 2) + P(x1 = 1 , x2= 3) + P(x2=0 , x1=2 ) + P(x2=1, x1=3) + P(x2=2, x1=4)

P[X1 > 2 + X2] = 0.04 + 0.04 + 0.05 + 0.02 + 0.05

P[X1 > 2 + X2] =0.20

d)

P( exactly 4) = 0.10

P( at least 4 ) = 0.10 + 0.06 + 0.01 + 0.02 + 0.04 + 0.07 + 0.00 + 0.01 + 0.05 + 0.09

P( at least 4 ) = 0.45