SOLUTION: A pair of dice is tossed and the larger of the two numbers showing is recorded. Find the expected value of this experiment. If both dice have the same number, use that number as

Algebra ->  Probability-and-statistics -> SOLUTION: A pair of dice is tossed and the larger of the two numbers showing is recorded. Find the expected value of this experiment. If both dice have the same number, use that number as       Log On


   

Question 379521: A pair of dice is tossed and the larger of the two numbers showing is recorded. Find the expected value of this experiment. If both dice have the same number, use that number as the highest. The answer is 4.47, but how do you do it. It is a probability distribution table, but how??
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
There are 36 possible outcomes.
Look at Die 1, Die 2, and Maximum.
1,+1,+1
1,+2,+2
1,+3,+3
1,+4,+4
1,+5,+5
1,+6,+6
2,+1,+2
2,+2,+2
2,+3,+3
2,+4,+4
2,+5,+5
2,+6,+6
3,+1,+3
3,+2,+3
3,+3,+3
3,+4,+4
3,+5,+5
3,+6,+6
4,+1,+4
4,+2,+4
4,+3,+4
4,+4,+4
4,+5,+5
4,+6,+6
5,+1,+5
5,+2,+5
5,+3,+5
5,+4,+5
5,+5,+5
5,+6,+6
6,+1,+6
6,+2,+6
6,+3,+6
6,+4,+6
6,+5,+6
6,+6,+6
Then construct the distribution counting the occurence of each value.
x, P%28x%29
1,1%2F36
2,3%2F36
3,5%2F36
4,7%2F36
5,9%2F36
6,11%2F36
The expected value mu is then,
mu=sum%28x%2AP%28x%29%2Cx=1%2C6%29
highlight%28mu=4.4722%29