Given that ` bar x`is the mean and `sigma^2`is the variance of n observations `x_1x_2`, ..., `x_n`. Prove that the mean and variance of the observations `a x_1,a x_2`, `a x_3,.........,a x_n`are `a bar x`and `a^2sigma^2`,

Explanation

Given, Mean `= \small \bar {x} and variance = \small \sigma^2`


Now, Let y_i be the the resulting observations if each observation is multiplied by

`a:

\\ \overline y_i = a\overline x_i \\ \implies \overline x_i = \frac{\overline y_i}{a}`


`\overline y =\frac{1}{n}\sum_{i=1}^ny_i = \frac{1}{n}\sum_{i=1}^nax_i`

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