The number of phone calls arriving at a switchboard can be represented by a Poisson random...
The number of phone calls arriving at a switchboard can be
represented by a Poisson random variable. The
average number of phone calls per hour is 1.7.
(a) Find the probability of getting a total of at least 3 phone
calls in the next hour.
(b) Find the probability of getting a total of at least 3 phone
calls in the next two hours.
(c) Find the probability that it is more than 30 minutes until the
next call arrives.
(d) Find the probability that the next call arrives between 15 and
30 minutes from now.
Homework Answers
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The number of phone calls arriving at a switchboard can be
represented by a Poisson random...
8.186 The number N(t) of phone calls arriving at a switchboard during the first t minutes...
8.186 The number N(t) of phone calls arriving at a switchboard during the first t minutes time that elapses between when you start your stopwatch and when the nth phone call arrives. after you start your stopwatch has a Poisson distribution with parameter 3.8t. Let W be the a) On average, how many phone calls arrive during the first t minutes? b) If it is known that Wi > t, what can be said about N(t)? Similarly, what would Wit...
Assume that the number of telephone calls arriving at a switchboard by time t (minutes) is...
Assume that the number of telephone calls arriving at a switchboard by time t (minutes) is described by Poison process {N(t)}. On average, one call comes in every 10 minutes. What is the probability that two or more calls will occur in 10 < t ≤ 20?
Suppose the number of phone calls passing through a particular cellular relay system, follows a Poisson...
Suppose the number of phone calls passing through a particular cellular relay system, follows a Poisson distribution with an average of 3 calls during a 1-min period. (A) Find the probability, p, that no call will pass through the relay system during a given 2-min period. (B) Find the probability that at least four minutes will pass before a call is passed through the relay system.
The number of calls arriving at a switchboard from noon to 1 p.m. during the business...
The number of calls arriving at a switchboard from noon to 1
p.m. during the business days Monday through Friday is monitored
for six weeks (i.e. 30 days). Let X be defined as the number of
calls during that one-hour period. The relative frequency of calls
was recorded and reported as:
Values 5 6 8 9 10 11 12 13 14 15
Rel. Freq. 0.067 0.067 0.100 0.133 0.200 0.133 0.133 0.067 0.033
0.067
Does the assumption of a Poisson...
Suppose the number of phone calls arriving at an answering service follows a Poisson process with...
Suppose the number of phone calls arriving at an answering service follows a Poisson process with the rate lambda = 60 (or equivalently, the interarrival times are iid exponential random variables with mean 1 minute). a.) Let T(I,j) denote the time interval from the ith arrival the jth arrival. The correlation between T(10,50) and T(20,60) is equal to ____________. b.) The correlation between T(0,20) and T(0,60) is equal to ________________.
1) The number of calls received at a certain information desk has a Poisson Distribution with...
1) The number of calls received at a certain information desk has a Poisson Distribution with an average of 6 calls per hour. (15 points) (a) Find the probability that there is at exactly one call during a 15 minute period. (You cannot use tables here - show all work) (b) Find the probability that at least 6 calls are received during a 30 minute period. (you may use tables here) ******************************** 2) Note that for the above problem, the...
1. The main office of a business receives phone calls according to a Poisson process, at...
1. The main office of a business receives phone calls according to a Poisson process, at an average rate of 3 calls per 10 minutes. What is the probability that over a 30 minute interval there will be at least 10 calls received ?
Exercise 2.3 The time between phone calls to a call center is exponentially distributed with mean...
Exercise 2.3 The time between phone calls to a call center is exponentially distributed with mean 60 seconds. (a) What is the probability that exactly 4 calls arrive in the next 2 minutes? (6) What is the probability that at least 2 calls arrive in the next 2 minutes? (c) What is the probability that no buses arrive in the next 2 minutes? (d) Given that a call has just arrived, what is the probability that the next call arrives...
Suppose the number of passengers arriving at an airline help desk follows a Poisson distribution. Passengers...
Suppose the number of passengers arriving at an airline help desk follows a Poisson distribution. Passengers arrive at the desk on average every 10 minutes. Answer the following: Enter your final answers in the boxes below. Show ALL working by uploading your handwritten working for this question to Laulima Dropbox within 15 minutes of completing your exam. Correct answers without working shown will not receive full credit. Note that writing Excel functions does NOT qualify as showing working. a) (2)...
The number of customers arriving at a fast food restaurant are modelled on a Poisson random...
The number of customers arriving at a fast food restaurant are modelled on a Poisson random variable X with parameter A = 1. The total time that it takes to serve k customers, k> 1, is modelled on a continuous random variable T that is uniform in 0,k+ 1]. (a) (2 points) Compute the probability P(T 1 (b) (2 points) Compute the expected value of T
The number of customers arriving at a fast food restaurant are modelled on a...
8.186 The number N(t) of phone calls arriving at a switchboard during the first t minutes time that elapses between when you start your stopwatch and when the nth phone call arrives. after you start your stopwatch has a Poisson distribution with parameter 3.8t. Let W be the a) On average, how many phone calls arrive during the first t minutes? b) If it is known that Wi > t, what can be said about N(t)? Similarly, what would Wit...
The number of calls arriving at a switchboard from noon to 1
p.m. during the business days Monday through Friday is monitored
for six weeks (i.e. 30 days). Let X be defined as the number of
calls during that one-hour period. The relative frequency of calls
was recorded and reported as:
Values 5 6 8 9 10 11 12 13 14 15
Rel. Freq. 0.067 0.067 0.100 0.133 0.200 0.133 0.133 0.067 0.033
0.067
Does the assumption of a Poisson...
1. The main office of a business receives phone calls according to a Poisson process, at an average rate of 3 calls per 10 minutes. What is the probability that over a 30 minute interval there will be at least 10 calls received ?
Exercise 2.3 The time between phone calls to a call center is exponentially distributed with mean 60 seconds. (a) What is the probability that exactly 4 calls arrive in the next 2 minutes? (6) What is the probability that at least 2 calls arrive in the next 2 minutes? (c) What is the probability that no buses arrive in the next 2 minutes? (d) Given that a call has just arrived, what is the probability that the next call arrives...
The number of customers arriving at a fast food restaurant are modelled on a Poisson random variable X with parameter A = 1. The total time that it takes to serve k customers, k> 1, is modelled on a continuous random variable T that is uniform in 0,k+ 1]. (a) (2 points) Compute the probability P(T 1 (b) (2 points) Compute the expected value of T
The number of customers arriving at a fast food restaurant are modelled on a...
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