Given that is the mean and is the variance of observations

MATHEMATICS · Subjective · CBSE · Mathematics · Statistics · Statistics

Problem

4. Given that

\bar{x}

is the mean and

\sigma^{2}

is the variance of

n

observations

x_{1}, x_{2}, \ldots, x_{n}

. Prove that the mean and variance of the observations

a x_{1}, a x_{2}, a x_{3}, \ldots, a x_{n}

are

a \bar{x}

and

a^{2} \sigma^{2}

, respectively,

(a \neq 0)