A fair dice is tossed.Let X denote the number that appears and let Y=1 if an odd number appears and Y=3 if an even number appears.Find (a) the probability function of X+Y (b) E(X+Y) (c) Var(X+Y) Solution x y x+y P(x+y) 1 1 2 1/6 2 3 5 1/6 3 1 4 1/6 4 3 7 1/6 5 1 6 1/6 6 3 9 1/6 E(x+y)= 1/6 *2 +1/6 *5 +1/6* 4 +1/6*7 +1/6*6 +1/6*9= 33/6=11/2 Var(x+y)= [(2-11/2)^2 +(5-11/2)^2 +(4-11/2)^2 +(7-11/2)^2 +(6-11/2)^2 +(9-11/2)^2]*1/6=4.92.

1. A fair dice is tossed.Let X denote the number that appears and let Y=1 if an odd number appears
and Y=3 if an even number appears.Find
(a) the probability function of X+Y
(b) E(X+Y)
(c) Var(X+Y)
Solution
x y x+y P(x+y) 1 1 2 1/6 2 3 5 1/6 3 1 4 1/6 4 3 7 1/6 5 1 6 1/6 6 3 9 1/6 E(x+y)=
1/6 *2 +1/6 *5 +1/6* 4 +1/6*7 +1/6*6 +1/6*9= 33/6=11/2 Var(x+y)= [(2-11/2)^2 +(5-11/2)^2
+(4-11/2)^2 +(7-11/2)^2 +(6-11/2)^2 +(9-11/2)^2]*1/6=4.92