Homework Soursegiven the probability distributions for variables X and Y sh
given the probability distributions for variables X and Y shown to the right, compute the terms below.
P(XiYi)
X
Y
0.4
100
300
0.6
300
100
a.
E(X)
and
E(Y)
b.
X
and
Y
c.
XY
d. E(X+Y)
| P(XiYi) | X | Y | |
| 0.4 | 100 | 300 | |
| 0.6 | 300 | 100 |
Solution
a.
E(X) = 0.4*100+0.6*300 = 220
E(Y) = 0.4*300+0.6*100 = 180
b.
Var(X) = 0.4*(100-220)2+0.6*(300-220)2 = 9600
X = sqrt(Var(X)) = 98
Var(Y) = 0.4*(300-180)2+0.6*(100-180)2 = 9600
Y = sqrt(Var(Y)) = 98
c.
E(XY) = 0.16*100*300+0.24*100*100+0.24*300*300+0.36*100*300 = 39600
Var(XY) = 0.16*(30000-39600)2+0.24*(10000-39600)2+0.24*(90000-39600)2+0.36*(30000-39600)2 867.84*106
XY = sqrt(Var(XY))29459.1
d.
E(X+Y) = E(X)+E(Y) = 220+180 = 400
| XY | 100*300 | 100*100 | 300*300 | 100*300 |
| P(XY) | 0.16 | 0.24 | 0.24 | 0.36 |
