The total time from arrival to completion of service at a fast-food outlet, Yi, and the...
The total time from arrival to completion of service at a fast-food outlet, Y, and the time spent in waiting in line before arriving at the service window, Y, have joint density function 1. fOz.yz) = Otherwise a) (9 pts) Find the joint density function for transformation method of section 6.6 i-2Y; and U.-y-Y; using the mo vanable b) (3pts) Without using integration or other calculus techniques, use the joint distribution found in part la to find the marginal distribution...
(Q6) The management at a fast-food outlet is interested in the joint behaviour of the random variables Yı, defined as the total time between a customer's arrival at the store and departure from the service window, and Y2, the time a customer waits in line before reaching the service window. Because Yſ includes the time a customer waits in line, we must have Yi > Y. The relative frequency distribution of observed values of Yi and Y2 can be modelled...
The management at a fast-food outlet is interested in the joint behavior of the randomvariables Y1 , defined as the total time between a customer’s arrival at the store and departurefrom the service window, and Y2 , the time a customer waits in line before reaching the servicewindow. Because Y1 includes the time a customer waits in line, we must have Y Y 1 2 ≥ . Therelative frequency distribution of observed values of Y1 and Y2 can be modeled...
Suppose that
Y1
is the total time between a customer's arrival in the store and
departure from the service window,
Y2
is the time spent in line before reaching the window, and the
joint density of these variables is
f(y1, y2) =
e−y1,
0 ≤ y2 ≤ y1 < ∞,
0, elsewhere.
We were unable to transcribe this image(a) Find the marginal density function for Y. f. (Y) = , where y, 21 Find the marginal density function for Y,...
1) A fast-food franchise is considering opening a drive-up window food service operation. Assume that customer arrivals follow a Poisson distribution ( interarrival times follow an exponential distribution), with a mean arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive up to the service window to pay for and receive their order. The following four...
Question 2 A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered: A single-channel operation...
A fast food franchise is considering a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution with a mean arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive up to the service window to pay for and receive their order. The following three service alternatives are being considered: a) A single-channel...
Problem 2. The time T (in hours past noon) until the arrival of the first taxi has Exp(6) distribution, and the time B until first bus is independent with Exp(4) distri- bution. (a) Write down the joint probability density function of T and B. (Pay attention to when it is 0 (b) Find the probability that the first taxi arrives before the first bus. (c) If you arrive at noon and take the first bus or taxi (whichever arrives first),...
The Burger Dome waiting line model studies the waiting time of customers at its fast-food restaurant. Burger Dome's single-server waiting line system has an arrival rate of 0.75 customers per minute and a service rate of 1 customer per minute. Adapt the Black Sheep Scarves spreadsheet shown below to simulate the operation of this waiting line. Make sure to use the random values for both interarrival and service times generated in the worksheet_12-23. Assuming that customer arrivals follow a Poisson...
In the Program Evaluation and Review Technique (PERT), we are
interested in the total time to complete a project that is
comprised of a large number of
subprojects. For illustration, let X1, X2, X3 be three
independent random times for
three subprojects. If these subprojects are in series (the
first one must be completed
before the second starts, etc.), then we are interested in the
sum Y = X1 +X2+X3.
If these are in parallel (can be worked on simultaneously),...