Question

Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x? Explain and give examples.

(please use another example and answer other than problems already answered.)

Answer 1

Expected value of a distribution need not be a possible value of X. It can be any value that fall within the range of the distribution.

Example 1: Consider the event of tossing a die.

The possible values of x are 1,2,3,4,5 and 6

Each of the value have a probability of 1/6

Expected value = (1+2+3+4+5+6)/6

= 3.5

3.5 is not a possible value of X

Example 2: Consider a binomial distribution with n = 4 and p = 0.3

Possible values of X are 0,1,2,3 and 4

Expected value of X = np

= 4x0.3

= 1.2

1.2 is not a possible value of x

In this example, if n = 0.25,

expected value = 4x0.25 = 1, which is a possible value of X

Expected value can be a possible value of X need not be in all cases.