Question

A random variable X is defined as the sum of the numbers
on the faces when two dice are thrown. Find the expected
value of x.​

Answer 1

Given :  A random variable X is defined as the sum of the numbers

on the faces when two dice are thrown.

To Find  :  the expected  value of x.​

Solution:  

Total possible outcome = 6 * 6 =  36

Sum can be from 2  to 12

 

E(X)        P(X)         E(X). P(X)

2            1/36             2/36

3           2/36             6/36

4           3/36            12/36

5           4/36           20/36

6           5/36          30/36

7           6/36           42/36

8           5/36          40/36

9           4/36          36/36

10           3/36        30/36

11          2/36          22/36

12            1/36         12/36

                               252/36

Expected Value  =  ∑ P(x).E(x)   = 252/36  = 7

expected  value of X  is 7

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