A lucky draw bowel contains three red balls and three white balls. Three balls were drawn at random with replacements. The random variable X will take the values from the number of red balls drawn at random. If one plays the following rule based game the amount earned by the player will be considered as the value of the random variable

Y. The rules are: The player will

(a) Receive Rs. 2 if he gets the Red ball in the first draw itself.

(b) Receive Rs. 4 if he gets the Red ball in the second draw

Receive Rs. 6 if he gets the Red ball in the third draw

(d) Receive a penalty of Rs. 2 if no red ball is drawn.

Find the joint p.m.f of the random variables X and Y

(ii) Check the independency

(iii)

Find E(X)