If a pair of dice is thrown and X denotes the sum of the numbers on them. Find the probability distribution of X.Also find the expectation of X. 

  SOLUTION: 

 In a single throw of a pair of dice the sum of the numbers on them can be 2,3,4….,12.So, X can assume values 2,3,4….,12.The probability distribution of X is as given below 

    X:  2       3        4        5       6        7      8        9      10     11    12 

P(X):1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36 

E(X)=1/36 x 2 + 2/36 x 3 + 3/36 x 4 + 4/36 x 5 +5/36 x 6 + 6/36 x 7

+ 5/36 x 8 +4/36 x 9 + 3/36 x 10 + 2/36 x 11 + 1/36 x 12 

E(X)=1/36[2+6+12+20+30+42+50+36+30+22+12] 

E(X)= 252/36 = 7