A market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in li
Posted: Thu May 05, 2022 9:19 pm
A market has both an express checkout line and a superexpress
checkout line. Let X1 denote the number of customers in line at the
express checkout at a particular time of day, and let X2 denote the
number of customers in line at the superexpress checkout at the
same time. Suppose the joint pmf of X1 and X2 is as given in the
accompanying table.
a. What is P(X1 = 1, X2 = 1) Þ; that is, the probability
that there is exactly one customer in each line?
b. What is P( X1 = X2) that is, the probability that the
numbers of customers in the two lines are identical?
c. Let A denote the event that there are at least two more
customers in one line than in the other line. Express A in terms of
X1 and X2, and calculate the probability of this event.
d. What is the probability that the total number of
customers in the two lines is exactly four? At least four?
e. Determine the marginal pmf of X1, and then calculate the
expected number of customers in line at the express checkout.
f. Determine the marginal pmf of X2.
g. By inspection of the probabilities P(X1 = 4), P(X2 = 0), and
P(X1 = 4, X2 = 0), are X1 and X2 independent random variables?
Explain.
X1 0 123 + 4 0 .08 .06 .05 .00 .00 .07 .15 .04 .03 .01 X2 2 .04 .05 .10 .04 .05 3 .00 .04 .06 .07 .06
checkout line. Let X1 denote the number of customers in line at the
express checkout at a particular time of day, and let X2 denote the
number of customers in line at the superexpress checkout at the
same time. Suppose the joint pmf of X1 and X2 is as given in the
accompanying table.
- A Market Has Both An Express Checkout Line And A Superexpress Checkout Line Let X1 Denote The Number Of Customers In Li 1 (24.43 KiB) Viewed 24 times
that there is exactly one customer in each line?
b. What is P( X1 = X2) that is, the probability that the
numbers of customers in the two lines are identical?
c. Let A denote the event that there are at least two more
customers in one line than in the other line. Express A in terms of
X1 and X2, and calculate the probability of this event.
d. What is the probability that the total number of
customers in the two lines is exactly four? At least four?
e. Determine the marginal pmf of X1, and then calculate the
expected number of customers in line at the express checkout.
f. Determine the marginal pmf of X2.
g. By inspection of the probabilities P(X1 = 4), P(X2 = 0), and
P(X1 = 4, X2 = 0), are X1 and X2 independent random variables?
Explain.
X1 0 123 + 4 0 .08 .06 .05 .00 .00 .07 .15 .04 .03 .01 X2 2 .04 .05 .10 .04 .05 3 .00 .04 .06 .07 .06