Question

Suppose a restaurant in town serves three fixed price dinners costing $12, $15, and $20. For a
randomly selected couple (
Penny
= X and
Leonard=
Y), the joint probability table for their selections
is given below.
Y
p(x,y)
12
15
20
12
.05
.05
.10
15
.05
.10
.35
20
0
.20
.10
a.
Find the marginal distributions of X and Y.
b.
Find Cov(X,Y) and Corr(X,Y). What is the strength
and direction of the correlation?
c.
Find the conditional distribution of X given Y=12.
d.
Find E(X|
Y=12) and Var(X|Y=12)