Suppose you're waiting for train A and your friend train B. Let X denote the wait...
Suppose you're waiting for train A and your friend train B. Let X denote the wait time for train A, Y the wait time for train B. Both X and Y are in minutes. Suppose that the two wait times have a joint probability density function p(x,y) = 12e-4x-3y. Suppose you're only willing to wait one hour for a train. What is the probability that you'll board your train after your friend boards hers? What is the probability that train A arrives after train B but before one hour has passed?
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Suppose you're waiting for train A and your friend train B. Let
X denote the wait...
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a...
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a mean rate of 4 per hour (60 minutes). Let Y denote the waiting time in minutes until the first bus arrives. (a) (5 points) What is the probability density function of Y? (b) (5 points) Suppose you arrive at the bus stop. What is the probability that you have to wait less than 5 minutes for the first bus? (c) (5 points) Suppose 10...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
Q2. Assume that the number of taxis that arrive at a busy intersection follows a Poisson...
Q2. Assume that the number of taxis that arrive at a busy intersection follows a Poisson distribution with a mean of 6 taxis per hour. Let X denote the time between arrivals of taxis at the intersection. (a) What is the mean of X? (b) What is the probability that you wait longer than one hour for a taxi? (c) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives...
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...
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...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
on page 496. Dew b) Exercise 9.100(a, 9.168 Let X and Y denote the x and...
on page 496. Dew b) Exercise 9.100(a, 9.168 Let X and Y denote the x and y coordinates, respectively, of a point selected at random d) the FPE a) Proposition 9.1 from the rectangle (a, b) x (c, d) = { (x, y) e R2 :a < x < b, c < y < d}. a Determine the joint CDF of the random variables X and Y b) Use part (a) to obtain the marginal CDFS of X and Y...
Problem #3: Suppose that the waiting time X (in seconds) for the pedestrian signal at a...
Problem #3: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a random variable with the following pdf. S (1 – x/76)8 0 < x < 76 otherwise If you use this crossing every day for the next 6 days, what is the probability that you will wait for at least 10 seconds on exactly 2 of those days? Problem #3: Round your answer to 4 decimals.
. Jan wins, ue OTCS LICO. 6.127 Consider two identical electrical components. Let X and Y denote the respective lifetim...
. Jan wins, ue OTCS LICO. 6.127 Consider two identical electrical components. Let X and Y denote the respective lifetimes of the two components observed at discrete time units (e.g.,every hour). Assume that the joint PMF of X and Y is px.y(x, y) = p (1 - p)*+-2 if x, y e N, and px.Y(x, y) 0 otherwise, where O <p< l. Use the FPF for two discrete random variables to determine the probability that one of the components lasts...
Can you solve 12 Thus, the expected time waiting is 5/6 hours (or 50 minutes) (Note...
Can you solve 12
Thus, the expected time waiting is 5/6 hours (or 50 minutes) (Note that it is wrong to reason like this: Alice expects to arrive at 12:30, Bob expects to arrive at 1:00: thus, we expeet that Bob will wait 30 mimutes for Alice.) (b). We want to compute the probability that Bob has to wait for Alice, which is P(Y < X), which we do by integrating the joint density, f(r,y), over the region where <...
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a mean rate of 4 per hour (60 minutes). Let Y denote the waiting time in minutes until the first bus arrives. (a) (5 points) What is the probability density function of Y? (b) (5 points) Suppose you arrive at the bus stop. What is the probability that you have to wait less than 5 minutes for the first bus? (c) (5 points) Suppose 10...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
Q2. Assume that the number of taxis that arrive at a busy intersection follows a Poisson distribution with a mean of 6 taxis per hour. Let X denote the time between arrivals of taxis at the intersection. (a) What is the mean of X? (b) What is the probability that you wait longer than one hour for a taxi? (c) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives...
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...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
on page 496. Dew b) Exercise 9.100(a, 9.168 Let X and Y denote the x and y coordinates, respectively, of a point selected at random d) the FPE a) Proposition 9.1 from the rectangle (a, b) x (c, d) = { (x, y) e R2 :a < x < b, c < y < d}. a Determine the joint CDF of the random variables X and Y b) Use part (a) to obtain the marginal CDFS of X and Y...
Problem #3: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a random variable with the following pdf. S (1 – x/76)8 0 < x < 76 otherwise If you use this crossing every day for the next 6 days, what is the probability that you will wait for at least 10 seconds on exactly 2 of those days? Problem #3: Round your answer to 4 decimals.
. Jan wins, ue OTCS LICO. 6.127 Consider two identical electrical components. Let X and Y denote the respective lifetimes of the two components observed at discrete time units (e.g.,every hour). Assume that the joint PMF of X and Y is px.y(x, y) = p (1 - p)*+-2 if x, y e N, and px.Y(x, y) 0 otherwise, where O <p< l. Use the FPF for two discrete random variables to determine the probability that one of the components lasts...
Can you solve 12
Thus, the expected time waiting is 5/6 hours (or 50 minutes) (Note that it is wrong to reason like this: Alice expects to arrive at 12:30, Bob expects to arrive at 1:00: thus, we expeet that Bob will wait 30 mimutes for Alice.) (b). We want to compute the probability that Bob has to wait for Alice, which is P(Y < X), which we do by integrating the joint density, f(r,y), over the region where <...
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