Given that  \displaystyle \bar{X} is the mean and  \displaystyle | Filo

Class 11

Math

Algebra

Statistics

582
150

Given that  is the mean and  is the variance of  observations . Prove that the mean and variance of the observations  are  and  respectively .

Solution: The given   observation are
Mean =
variance =
....(i)
If each observation is multiplied by a and the new observation are  then

Therefore mean of the observation,  is
Substituting the values of  and  in (1) we obtain

Thus the variance of the observation  is
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