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 the probability that the numbers of customers in the two lines are identical?(4) What is the probability that the total number of customers in the two lines is at least four?(5) What is the probability that the express line has no customer?(6) Given that there are at least two customers in the express line, what is the conditional probability that the regular line has no customer?
A grocery store has both a regular checkout line and an express checkout line. Let 푋1be...
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 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 ...
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 &...
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...
Formulas 1.) (5 pt.) At a grocery store customers in the checkout line may use a credit card. The probability they will use a credit card is 80%. There are four customers in a line. Let X be the random variable (R.V.) denoting the number of customers out of the four who use a credit card. Determine the probability mass function (pmf) for X and use it to construct both graphically and numerically the cumulative distribution function (CDF) for X....
Customer arrives at a grocery store to checkout counter according to a Poisson process with rate per minute. Each customer carries a number of items that is uniformly distributed between 1 and 40. The store has 2 checkout counters, each capable of processing items at a rate of 15 per minute. To reduce the customer wait in queue, the store manager considers dedicating a one of the two counters to customers with x items or less and dedicating one of...
A quality control specialist at Albertsons grocery knows that on average each grocery store receives 5 complaints from customers per week. (a) What is the probability that for a single store exactly 5 customer complaints are received in a given week? (b) What is the probability that for a single store at least 3 customer complaints are received in a given week? (c) What is the probability that for a single store no more than 3 customer complaints are received...
Customer arrivals at a checkout counter in a department store have a Poisson distribution with an average of seven per hour. For a given hour, find the probability that a. exactly nine customers arrive b. no more than three customers arrive c. at least two customers arrive
A certain small grocery store has a single checkout stand with a full-time cashier manning it. Customers arrive at the stand randomly (i.e. Poisson input process) at a mean rate of 30 per hour. When there is only one customer at the stand, he is processed by the cashier alone, with an expected service time of 1.5 minutes. However, the stock boy has been given standard instructions that whenever there is more than one customer at the stand, he is...
Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. 1 0.15 2 0.30 3 0.20 4 0.10 5 0.05 P(x) 0.20 Send data to Excel Part 1 of 7 (a) Find P(5). P(5) = 0 Part 2 of 7 (b) Find P(No less than 4). P(No less than 4) = Part 3 of 7 (c) Find the probability that no one is in line....