Question

If X is a random variable such that P(X = −2) = P(X = −1) = P(X = 2) = P(X = 1) = `1/6` and P(X = 0) = `1/3`, then the mean of X is ______.

Options

• `5/3`

• 1

• 0

• `3/5`

Answer 1

If X is a random variable such that P(X = −2) = P(X = −1) = P(X = 2) = P(X = 1) = `1/6` and P(X = 0) = `1/3`, then the mean of X is 0.

Explanation:

P(X = −2) = P(X = −1)

= P(X = 2) = P(X = 1) = `1/6`

& P(X = 0) = `1/3`

Mean = (−2).P(X = −2) + (−1) P(X = −1) + 0.

P(X = 0) + 1.P(X = 1) + 2Pp(X = 2)

= `-2 xx 1/6 - 1/6 = 0 + 1/6 + 2 xx 1/6`

= Mean = 0