Question

The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.

विकल्प

• 5

• 6

• 7

• 8

Answer 1

The expected value of the sum of two numbers obtained when two fair dice are rolled is 7.

Explanation:

The sample space of the experiment consists of 36 elementary events in the form of ordered pairs (x_i, y_i), where x_i = 1, 2, 3, 4, 5, 6 and y_i = 1, 2, 3, 4, 5, 6.
The random variable X, i.e., the sum of the numbers on the two dice takes the values 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12.

X = xi	P(xi)	xiP(xi)
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)`
		E(X) = \[\sum\limits_{i=1}^{n} x_i\text{P}(x_i)\] = `(252)/(36)` = 7