Let X be a random variable that is uniformly chosen from the set of a positive odd number less than 100. The expectation E[x], is

Concept:

E[x] = Mean of Random variable X

X = discrete random variable

The expectation is given by the formula:

x_i = i^th random variable

P(x_i) = Probability of x_i

Calculation:

X: set off positive odd numbers less than 100, i.e.

X: {1, 3, 5, 7, 9, 11, …, 93, 95, 97, 99}

Since X is uniformly chosen, the probability of each random variable will be:

Where n = total number of random variables

Here, n = number of odd numbers less than 100

n = 50

Clearly an AP is formed with n = 50, a = 1 and l = 99.

The sum of an AP is given by the formula:

E[x_i] = 50