1.A researcher suspected that the number of alcoholic beverages consumed by statistics students in a particular evening might depend on how many practice problems a student had solved during the same day. This table shows joint probabilities for various numbers of drinks and statistics problems.

Number of Practice Problems

Number of Drinks0 1 23

00.07 0.090.06 0.01

10.07 0.060.07 0.01

20.06 0.070.14 0.03

30.02 0.040.16 0.04

(a)Let the random variable X be the number of stats problems solved by a particular student in one day. What is the estimated probability function for X? (A probability function for X is a list of all the possible values for X, and the associated probability for each value.)

(b)Let the random variable Y be the number of alcoholic beverages consumed by a particular student in one evening. What is the estimated probability function for Y?

(c)What are the estimated means and standard deviations of X and Y?

(d)What is the conditional probability function for Y, given that X = 3? (A conditional probability function for Y, given that X = 3 is a list of all the possible values for Y, and the associated probability for each value, under the assumption that X is known to be 3.)