Answer :

The given n observations in the question are x_{1}, x_{2},…..x_{n}

Also, mean =

And, variance = σ^{2}

We know that,

According to the condition given in the question, if each of the observation is being multiplied by a and the new observation are y_{i} the, we have:

y_{i} = ax_{i}

Hence, mean of the observations ax_{1}, ax_{2},…..ax_{n} is a

Now, by substituting the values of x_{i} and in (i), we get:

Hence, the variance of the given observations ax_{1}, ax_{2},….ax_{n} is a^{2}σ^{2}

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