Suppose you are in line at Costco and there are 100 people in front of you....
Suppose you are in line at Costco and there are 100 people in front of you. Assume that the time it takes each person in front of you to be served follows an Exponential distribution with expected value 4 (ignore units). Let X be the total time you wait for all 100 people in front of you to be served.
What is the moment generating function of X?
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Suppose you are in line at Costco and there are 100 people in
front of you....
You get in line at a popular tobacco shop and notice that there are many people in line ahead of you. During the next 10...
You get in line at a popular tobacco shop and notice that there are many people in line ahead of you. During the next 10 minutes you notice that 10 more customers have arrived. You now count 18 people ahead of you in line. Use Little's Law to estimate the total amount of time (in minutes) you should expect to wait to be served.
can you also show how to do this on excel? Costco installs automobile tires on a...
can
you also show how to do this on excel?
Costco installs automobile tires on a first-come first-serve basis. The total time a customer needs to wait for the installation to be completed follows the normal distribution with a mean time of 106.3 minutes and a standard deviation of 18.5 minutes. What is the probability that a randomly selected customer will wait 125 minutes for his or her tires to be installed?
The process of being served at a bank consists of two parts—the time waiting in line...
The process of being served at a bank consists of two parts—the time waiting in line and the time it takes to be served by the teller. Suppose that the time waiting in line (X) has an expected value of 4.21 minutes, with a standard deviation of 1.1 minutes, the time it takes to be served by the teller (Y) has an expected value of 6.65 minutes, with a standard deviation of 1.32 minutes, and the correlation coefficient between the...
Suppose the waiting time, in minutes, at a checkout line in a local super market follows...
Suppose the waiting time, in minutes, at a checkout line in a local super market follows a Uniform distribution in the interval (1,6) a. How long is a randomly chosen customer at the super market expected to wait at the checkout counter? b. What is the probability that a randomly chosen customer at the super market will wait between 2 and 5 minutes to be checked out? c. Suppose a random sample of 100 customers is taken at the super...
Suppose your wait time for shuttle bus follows an exponential distribution with u = 5. (a)...
Suppose your wait time for shuttle bus follows an exponential distribution with u = 5. (a) What is the probability that you have to wait longer than 10? (b) Given you already waited 10 minutes, what is the probability that you have to wait for another 10 more minutes? (c) Let X be exponentially distributed with parameter 1/u. Prove that P(X >a+b|X >a)=P(X >b)
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the...
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the same time. Bob insists Mary go ahead of him. Let X denote the time (in minutes) until Mary can be served and Y be the time (in minutes) until Bob is served. Suppose the joint density of X and Y is f(x.y)-1ootherwise Find the moment-generating function of U =-aln(X/Y) What is the distribution of U?
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the...
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the same time. Bob insists Mary go ahead of him. Let X denote the time (in minutes) until Mary can be served and Y be the time (in minutes) until Bob is served. Suppose the joint density of X and Y is f(x, y) 0 , otherwise Find the moment-generating function of U --aln(X/Y). What is the distribution of U?
Using MGF 11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter...
Using MGF
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the same time Bob insists Mary go ahead of him. Let X denote the time (in minutes) until Mary can be served and y be the time (in minutes) until Bob is served. Suppose the joint density of X and Y is 0 otherwise Find the moment-generating function of U =-aln(X/Y), what is the distribution of U?
3. Let th e random variable Ti denote the time you must wait to place your order in a fast-food restaurant, let Tz denote the time that it takes to place your order after you reach the counter, le...
3. Let th e random variable Ti denote the time you must wait to place your order in a fast-food restaurant, let Tz denote the time that it takes to place your order after you reach the counter, let s denote the time that it takes to receive vour food after you've placed your order, and let T enote the time that it takes to east vour food after you've received it. Assume that all of these random variables are...
Let us consider a country of 100 people. Each person can produce 5 units of Good...
Let us consider a country of 100 people. Each person can produce 5 units of Good X or 10 units of Good Y a. b. C. d, e. Draw the PPF of the country, with Good X on x-axis and Good Y on y-axis. Write out the function of the PPF. What is the slope of the PPF? What does the slope of the PPF mean? if the market prices are PX-Py-1, at which point will the economy produce? (hard)...
can
you also show how to do this on excel?
Costco installs automobile tires on a first-come first-serve basis. The total time a customer needs to wait for the installation to be completed follows the normal distribution with a mean time of 106.3 minutes and a standard deviation of 18.5 minutes. What is the probability that a randomly selected customer will wait 125 minutes for his or her tires to be installed?
Suppose your wait time for shuttle bus follows an exponential distribution with u = 5. (a) What is the probability that you have to wait longer than 10? (b) Given you already waited 10 minutes, what is the probability that you have to wait for another 10 more minutes? (c) Let X be exponentially distributed with parameter 1/u. Prove that P(X >a+b|X >a)=P(X >b)
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the same time. Bob insists Mary go ahead of him. Let X denote the time (in minutes) until Mary can be served and Y be the time (in minutes) until Bob is served. Suppose the joint density of X and Y is f(x.y)-1ootherwise Find the moment-generating function of U =-aln(X/Y) What is the distribution of U?
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the same time. Bob insists Mary go ahead of him. Let X denote the time (in minutes) until Mary can be served and Y be the time (in minutes) until Bob is served. Suppose the joint density of X and Y is f(x, y) 0 , otherwise Find the moment-generating function of U --aln(X/Y). What is the distribution of U?
Using MGF
11. (5 marks) Two customers, Bob and Mary, arrive at an occupied service counter at the same time Bob insists Mary go ahead of him. Let X denote the time (in minutes) until Mary can be served and y be the time (in minutes) until Bob is served. Suppose the joint density of X and Y is 0 otherwise Find the moment-generating function of U =-aln(X/Y), what is the distribution of U?
3. Let th e random variable Ti denote the time you must wait to place your order in a fast-food restaurant, let Tz denote the time that it takes to place your order after you reach the counter, let s denote the time that it takes to receive vour food after you've placed your order, and let T enote the time that it takes to east vour food after you've received it. Assume that all of these random variables are...
Let us consider a country of 100 people. Each person can produce 5 units of Good X or 10 units of Good Y a. b. C. d, e. Draw the PPF of the country, with Good X on x-axis and Good Y on y-axis. Write out the function of the PPF. What is the slope of the PPF? What does the slope of the PPF mean? if the market prices are PX-Py-1, at which point will the economy produce? (hard)...
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