Question

Two balls are drawn in succession without replacement from a bag containing
2 red balls, 1 green balls and 3 green balls. Let X and Y denote the number
of red and green balls respectively. Find
a) f(x,y) the expression for the joint p.d.f of X and Y [5 Marks]
b) f(x) the expression for the marginal pdf of X [5 Marks]
c) f(y) the expression for the marginal pdf of Y [5 Marks]
d) f(y/x), the expression for the conditional pdf of Y given X [6 Marks]
e) Cov(X,Y), the covariance of X and Y [10 Marks]
f) ρXY , the correlation coefficient of X an Y [5 Marks]
g) Is X and Y independent? Prove or disapprove

Answer 1

The number of ways of choosing 2 balls from 2+1+3=6 balls is .

a) The joint PMF is

The above joint PMF can be written as

b) The marginal PDF of X is

c) The marginal PDF of Y is

d) The conditional PDF is

We are required to solve only 4 parts. Please post the remaining questions as another post.