Q. 44.6( 13 Votes )

Given that

Answer :

The given n observations in the question are x1, x2,…..xn

Also, mean =


And, variance = σ2


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 yi the, we have:


yi = axi








Hence, mean of the observations ax1, ax2,…..axn is a


Now, by substituting the values of xi and in (i), we get:




Hence, the variance of the given observations ax1, ax2,….axn is a2σ2


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