Question 1174545: Can you explain this problem to me?
EXAMPLE 4: Suppose a pair of dice are rolled. What is the expected value of the random variable which assigns to each element in the sample space the sum of the dice?
I understand the range of (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
I don't understand how they got the following:
Px(2)= P (x=2) = 1/36
Px(3)= P (x=3) = 2/36
Px(8)= P (x=8) = 5/36
Px(9)= P (x=9) = 4/36
Found 2 solutions by ikleyn, ewatrrr:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
If you want to learn this subject, look into the lesson
- Rolling a pair of fair dice
in this site. You will find there many other similar solved problems.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Solved problems on Probability".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
Answer by ewatrrr(24785)  (Show Source):
You can put this solution on YOUR website!
Hi
One can 'count' the expected value from the Chart below,
which details the '36' ways of rolling a pair of dice.
Px(2)= P (x=2) = 1/36
Px(3)= P (x=3) = 2/36
Px(8)= P (x=8) = 5/36
Px(9)= P (x=9) = 4/36
-----------------
___1__2__3__4__5__6
1|_2__3__4__5__6__7
2|_3__4__5__6__7__8
3|_4__5__6__7__8__9
4|_5__6__7__8__9__10
5|_6__7__8__9__10_11
6|_7__8__9_10__11_12
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) etc...
Wish You the Best in your Studies.
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