Suppose the number of phone calls arriving at an answering service follows a Poisson process with...

Question

Question

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 ________________.

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

ANSWER::

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

ANS:: 3/4

b.)

The correlation between T(0,20) and T(0,60) is equal to

ANS:: sqrt(1/3)

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU

Add a comment

Answer 2

Similar Homework Help Questions

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....
The number of cars arriving at a gas station follows a Poisson distribution with μ=20 customers...

The number of cars arriving at a gas station follows a Poisson distribution with μ=20 customers in an hour. Let X= waiting time (in minutes) between two arrivals. What is the distribution of X? What is the probability of having no arrivals in a 10-minute interval? What is the probability that the next arrival is within 5 minutes?
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...

Suppose the number of phone calls arriving at an answering service follows a Poisson process with...

Homework Answers

Add Answer to:
Suppose the number of phone calls arriving at an answering service follows a Poisson process with...

Post as a guest

Earn Coins

The number of phone calls arriving at a switchboard can be represented by a Poisson random...

The number of cars arriving at a gas station follows a Poisson distribution with μ=20 customers...

8.186 The number N(t) of phone calls arriving at a switchboard during the first t minutes...

Suppose the number of phone calls arriving at an answering service follows a Poisson process with...

Homework Answers

Add Answer to: Suppose the number of phone calls arriving at an answering service follows a Poisson process with...

Post as a guest

Earn Coins

The number of phone calls arriving at a switchboard can be represented by a Poisson random...

The number of cars arriving at a gas station follows a Poisson distribution with μ=20 customers...

8.186 The number N(t) of phone calls arriving at a switchboard during the first t minutes...

Add Answer to:
Suppose the number of phone calls arriving at an answering service follows a Poisson process with...