A real estate agent is interested in the relationship between the number of lines in a newspaper advertisement for an apartment and the volume of inquiries from potential renters. Let volume of inquiries be denoted by the random variable X, with the value 0 for little interest, 1 for moderate interest, and 2 for strong interest. The real estate agent used historical records to compute the joint probability distribution shown in the accompanying table.

a. Find the joint cumulative probability at X = 1, Y = 4, and interpret your result.
b. Find and interpret the conditional probability distribution for Y, given X = 0.
c. Find and interpret the conditional probability distribution for X, given Y = 4.
d. Find and interpret the covariance between X and Y.
e. Are number of lines in the advertisement and volume of inquiries independent of one another?

Number Number of Inquiries (X) of Lines () 0 0.09 0.07 0.03 0.14 0.23 0.10 2 0.07 0.16 0.11