4) Check in each case whether the given function can serve as the probability distribution of an appropriate random variable.

6.4) Check in each case whether the given function can serve as the probability distribution of an appropriate random variable.

(a) f (x) = (2/x)/4   for x = 0, 1, 2

(b) f (x) =(x-2)/9   for x = 1, 2, 3, 4, 5, 6

(c) f (x) = (x^2-6x+9)/10  for x = 1, 2, 3, 4, 5

(d) f (x) = (x^2-6x+8)/5  for x = 1, 2, 3, 4, 5

6.8) A store advertised a clearance sale, and the probability is 0.20 that any one customer will make a purchase. Use Table 1 to determine the probability that in a random sample of eight shoppers

(a) three will make a purchase;

(b) two will make a purchase;

(c) one will make a purchase;

(d) none will make a purchase;

6.28) A certain squad of the U.S Army has seven male five female enlisted personnel, of whom six randomly selected to form an honor guard. Use the formula for hypergeometric distribution and Table X (Binomial Coefficients) to determine the probabilities that

(a) three personnel of the honor guard will be male, and three will be female;

(b) five will be male and one will be female.

6.36) Among the 120 employees of a company, 45 are member of a clerical works union, and the others are members of the typesetter's union. If 5 of the employees are chosen by lot to serve on a grievance committee, find the probability that 2 of them will be members of the clerical workers union and other 3 members of the typesetter's union, using

(a) the formula for the hypergeometric distribution;

(b) the binomial distribution as an approximation.