A real estate agent is interested in the relationship between the number of lines in a news- paper advertisement for an apartment and the volume of enquiries from potential renters. Let volume of enquiries be denoted by the random variable X, with the value 0 for little in- terest, 1 for moderate interest, and 2 for heavy interest. The real estate agent estimated the joint probability function shown in the accompanying table. NUMBER OF LINES (Y) 3 4 5 VOLUME OF ENQUIRIES (X)

(a) Find the joint cumulative probability function at X 1, Y 4, and interpret your result.

(b) Find and interpret the conditional probability function for Y, given X-0.

(c) Find and interpret the conditional probability function for X, given Y-5.

(d) Find and interpret the covariance between X and Y.

(e) Are number of lines in the advertisement and volume of enquiries independent of one another?