Question

If r.v. X assumes values 1, 2, 3, ..., n with equal probabilities then E(X) = `(n + 1)/(2)`.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

X	1	2	3	....	n
P(X)	`1/n`	`1/n`	`1/n`		`1/n`

E(X) = `sum x_i * P(x_i)`

= `1(1/n) + 2(1/n) + 3(1/n) + .... + n(1/n)`

= `(1)/n (1 + 2 + 3 + .... + n)`

= `(1)/n * (n(n + 1))/(2)`

= `(n + 1)/(2)`