A Pair of fair dice is rolled at a time the random variable X is the maximum of the two numbers shown on the dice the mean of X is
Answers
Given : A Pair of fair dice is rolled at a time the random variable X is the maximum of the two numbers shown on the dice
To find : Mean of X
Solution:
A Pair of fair dice is rolled
Total Possible outputs 36
(1 ,6) (2 , 6) , (3 ,6) , (4 ,6) , (5 ,6) , (6 , 6 ) (6 , 5 ) (6 , 4) , ( 6 , 3) , ( 6 , 2) , ( 6, 1) output = 6 ( 11 cases)
(1 ,5) (2 , 5) , (3 ,5) , (4 ,5) , (5 ,5) , (5 ,4) , ( 5 ,3 ) , ( 5 , 2) , ( 5, 1) output = 5 ( 9 cases)
(1 ,4) (2 , 4) , (3 ,4) , (4 ,4) , (4 , 3) , ( 4, 2) , ( 4 , 1) - ouput 4 - ( 7 cases)
(1 , 3 ) , ( 2, 3) , ( 3, 3) , ( 3 , 2) , ( 3, 1) - output 2 (5 cases)
(1 , 2) , ( 2, 2) , ( 2, 1) - output 2 ( 3 cases)
(1 , 1) - ouput 1 1 case
X Probability
6 11/36
5 9/36
4 7/36
3 5/36
2 3/36
1 1/36
Mean of X = 6 ( 11/36) + 5(9/36) + 4(7/36) + 3(5/36) + 2(3/36) + 1(1/36)
= (66 + 45 + 28 + 15 + 6 + 1 )/36
= 161/36
= 4.47
4.47 is mean of X
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