Question

Please answer all parts.

7. A sample statistic is an estimator of the population parameter, if the mean of the sampling distribution for the sample statistic is the 8. A distribution has a mean of 12 and a variance of 250. Find the second moment about the origin. Answer:

Answer 1

Question 7

We know that a sample statistic is used to infer about a parameter of the population; a statistic is said to be an unbiased estimator of the parameter, if the mean of the sampling distribution for the statistic is same as the population parameter.

Therefore, the complete statement is

A sample statistic is an UNBIASED estimator of the population parameter, if the mean of the sampling distribution for the sample statistic is the POPULATION PARAMETER.

Question 8

A distribution has a mean of 12 and a variance of 250.

If X denotes the population, then

$E(X)=12$

$Var(X)=250$

Now, we have to find the second moment about the origin for X.

So, basically we have to find

$E(X^{2})$

Now, according to the definition of Variance of X,

$Var(X)=E(X^{2})-E^{2}(X)$

$or,250=E(X^{2})-12^{2}$

$or,E(X^{2})=250+12^{2}$

$or,E(X^{2})=250+144=394$

So, the answer is

The second moment about the origin is 394.