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Problem 2. The time T (in hours past noon) until the arrival of the first taxi...
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...
Problem 4 Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria Bob's arrival time, denoted by X, measured in minutes after 12 noon, is a uniform random variable betrwen 0 a...
Problem 4 Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria Bob's arrival time, denoted by X, measured in minutes after 12 noon, is a uniform random variable betrwen 0 and Go minutes. The same for Alice's amial time, denoted by Y Bob's and Alice's arrival times are independent. We are interested in the waiting time i. What is the probability that W 10 if X 15? ii. What is the probability that...
The time between arrivals of taxis is exponentially distributed with a mean of 10 minutes. a)...
The time between arrivals of taxis is exponentially distributed with a mean of 10 minutes. a) You are fourth in line looking for a taxi. What is the probability that exactly 3 taxis arrive within one hour? b) Suppose the other three parties just decided to take the subway and you are now the first in line for the next taxi. Determine the time t such that the probability you wait less than t minutes from now until the next...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a ga...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a ga...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a ga...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Reason arrivals poisson and time continuous - exp prob Mode 1 1. The time until the...
Reason arrivals poisson and time continuous - exp prob Mode 1 1. The time until the next arrival at a gas station is modeled as an exponential random with mean 2 minutes. An arrival occurred 30 seconds ago. Find the probability that the next arrival occurs within the next 3 minutes. X= Time until next assival xu Expoential prob. Model Find: p(x-3) = P( ) e mean = 2 minutes = Arrival 30 sec ago = Next arrival w/in 3...
Problem 8 The time (in minutes) until the next bus departs a major bus depot follows...
Problem 8 The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution from 30 to 48 minutes. Let X denote the time until the next bus departs. a. The distribution is Uniform and is continuous b. The mean of the distribution is u = 39 c. The standard deviation of the distribution is 0 = d. The probability that the time until the next bus departs is between 30 and 40 minutes is...
The arrival time t(in minutes) of a bus at a bus stop is uniformly distributed between 10:00 A.M. and 10:03 A.M.
The arrival time t(in minutes) of a bus at a bus stop is uniformly distributed between 10:00 A.M. and 10:03 A.M. (a) Find the probability density function for the random variable t. (Let t-0 represent 10:00 A.M.) (b) Find the mean and standard deviation of the the arrival times. (Round your standard deviation to three decimal places.) (с) what is the probability that you will miss the bus if you amve at the bus stop at 10:02 A M ? Round your answer...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
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...
Problem 4 Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria Bob's arrival time, denoted by X, measured in minutes after 12 noon, is a uniform random variable betrwen 0 and Go minutes. The same for Alice's amial time, denoted by Y Bob's and Alice's arrival times are independent. We are interested in the waiting time i. What is the probability that W 10 if X 15? ii. What is the probability that...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Reason arrivals poisson and time continuous - exp prob Mode 1 1. The time until the next arrival at a gas station is modeled as an exponential random with mean 2 minutes. An arrival occurred 30 seconds ago. Find the probability that the next arrival occurs within the next 3 minutes. X= Time until next assival xu Expoential prob. Model Find: p(x-3) = P( ) e mean = 2 minutes = Arrival 30 sec ago = Next arrival w/in 3...
Problem 8 The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution from 30 to 48 minutes. Let X denote the time until the next bus departs. a. The distribution is Uniform and is continuous b. The mean of the distribution is u = 39 c. The standard deviation of the distribution is 0 = d. The probability that the time until the next bus departs is between 30 and 40 minutes is...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
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