Question 1

A.

Let f(X) be the pdf for the random variable X and let h(Y) be the pdf for the random variable Y.

Let g(X,Y) be their joint pdf and X and Y be independent.

Which of the following follows directly from these statements?

A.g=hf

B.g=h/f

C.g=f/h

D.g=f+h

B.

It is of interest to estimate the mean income of a population. A random sample of size 100 is intended to be selected from the population and the sample mean of their income is to be used to estimate the parameter of interest. Which of these statements are correct based only on the information given in the problem?

Statement 1: The standard deviation of the sample mean is less than the standard deviation of income.

Statement 2: The sample mean may be approximated as being Normally distributed.

A.Statement 1 only

B.Neither Statement 1 nor Statement 2

C.Both Statement 1 and Statement 2

D.Statement 2 only