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

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