A certain 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.
x2 | |||||
0 | 1 | 2 | 3 | ||
x1 | 0 | 0.09 | 0.07 | 0.04 | 0.00 |
1 | 0.05 | 0.15 | 0.04 | 0.04 | |
2 | 0.05 | 0.04 | 0.10 | 0.06 | |
3 | 0.00 | 0.03 | 0.04 | 0.07 | |
4 | 0.00 | 0.02 | 0.05 |
0.06 |
(a) What is P(X1 = 1, X2 = 1), 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?
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?
A certain market has both an express checkout line and a superexpress checkout line. Let X1...
5.1A certain market has both an express checkout line and a superexpress checkout line. Let X, 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. $$ \begin{array}{cc|cccc} & & \multicolumn{3}{|c} {x_{2}} \\ & & 0 & 1 & 2 &...
3. A certain market has both an express checkout line and a superexpress checkout line. Let X, denote the number of customers in line at the express checkout at a particular time of day, and let X, denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X and X, is as given in the accompanying table. 0 0.08 0.06 0.05 0 0 1 0.07 0.15 0.04 0.03 0.01 2...
A grocery store has both a regular checkout line and an express checkout line. Let 푋1be the number of customers in the regular checkout line at a particulartime of day, and let 푋2be the number of customers in the express checkout lineat the same time. The joint PMF of 푋1and 푋2is given in the table below. 푋20123푋10.08.07.04.001.06.15.05.042.05.04.10.063.00.03.04.074.00.01.05.06(1) How do you know this is a valid PMF?(2) What is the probability that there areexactly two customers in each line?(3) What is...
A small market has two checkout lines, regular and express. Let X be the number of customers in line at a regular checkout, and Y that at the express checkout. At a particular time of the day, the joint probability mass function of X and Y is given by (a) Find the probability that the total number of customers at a given time is at most 1, that is find P(X+Y≤1) [1] (b) Fill in the table with the marginal distribution of...
The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. 3 2 0.29 4 0.09 5 0.07 0.20 х 0 1 P(x) 0.09 0.26 Find P2 or fewer). 0 0.65 O 0.35 O 0.64 O 0.29
A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. x 0 1 2 3 4 5 6 p(x) 0.12 0.15 0.20 0.25 0.18 0.07 0.03 Calculate the probability of each of the following events. (a) {at most three lines are in use} (b) {fewer than three lines are in use} (c) {at least three lines are...
Example 5.5 (Discrete case). Let X be a discrete random variable, r be its observation, and the pmf of X be given by 1 2345678 9 10 ac f (x:0) 0 0.58 0.02 0.05 0.03 0.11 0.01 0.07 0.04 0.09 f( 1) 0.6 0 0.06 0.08 0.03 0.01 0.04 0.12 0.02 0.04
explain as much as possible, thanks A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. p(x, y) 0 0 y 1...
0 points DevoreStat9 3.E 013 A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table 6. -1 My Notes p(x) 0.11 0.15 0.20 0.25 0.19 0.07 0.03 Calculate the probability of each of the following events. (a) fat most three lines are in use) (b) fewer than three lines are in use (c) sat least three lines...
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 0 0.05 0.01 1 0.10 0.06...