PROBLEM 19E

Let X have a uniform distribution U(0, 2), and let the conditional distribution of Y, given that X = x, be U(0, x2).

(a) Determine f (x, y), the joint pdf of X and Y.

(b) Calculate fY(y), the marginal pdf of Y.

(c) Compute E(X | y), the conditional mean of X, given that Y = y.

(d) Find E(Y | x), the conditional mean of Y, given that X = x.

POWERPOINT 7 ● distribution of sample means = the total number of sample means that are obtained for all of the possible random samples of a particular size (n) from a population ● we are examining the spread of our sample means ● statistics (values associated with a sample) have sampling variability associated with them ● sampling distribution = distribution of statistics obtained by selecting all the possible samples of a specific size from a population ● sample means pile up around the population mean ● sample means tend to form a normal distribution ● the larger the sample size, the closer the sample means will be to the population means ● it is virtually impossible to