Question

1. Suppose the number of messages arriving on a communication line seems to be describable by...

1. Suppose the number of messages arriving on a communication line seems to be describable by a Poisson Random Variable with an average arrival rate of 10 messages/second. Determine the following:

a. The probability that no messages arrive in a one second period.

b. The probability that 1 message arrives in a one second period.

c. The probability that 2 messages arrives in a one second period.

d. The probability that 3 messages arrives in a one second period.

e.The probability that 10 messages arrive in a one second period.

f. The probability that 4or more messages arrive in a one second period.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The number of buses arriving at the bus stop for T minutes is defined as a...
The number of buses arriving at the bus stop for T minutes is defined as a random variable B. The average (expected value) of random variable B is T / 5. (1)A value indicating the average number of occurrences per unit time in the Poisson distribution. What is the average rate of arrival per second? (2)find PMF of B (3)Find the probability of 3 buses arriving in 2 minutes (4)Find the probability that the bus will not arrive in 10...
The average number of customers arriving at a bank branch is eight per hour. Assume that...
The average number of customers arriving at a bank branch is eight per hour. Assume that customer arrivals follow a Poisson process. The bank opens at 9:00 am in the morning. Answer the following questions accordingly. a) What is the probability that the first customer will arrive after 9:10 am? b) Suppose that it is now 9:15 and the first customer has arrived at 9:12 am. What is the probability that the second customer will arrive after 9:25 am? c)...
The number of cars arriving at a gas station can be modelled by Poisson distribution with...
The number of cars arriving at a gas station can be modelled by Poisson distribution with the average rate of 5 cars per 10 minutes. a. The probability that one car will arrive to a gas station in a 5 -minute interval is _________ b. The probability that at least one car will arrive to the gas station in a 10 - minute interval is ______
The number of cars arriving at a petrol station in a period of t minutes may...
The number of cars arriving at a petrol station in a period of t minutes may be assumed to have a Poisson distribution with mean 720t. Use this information to answer questions 31-32. Find the probability that exactly 12 cars will arrive in one and half hours. Find the probability that more than 24 cars will arrive in an hour.
The number of emails arriving at a server during any one hour period is known to...
The number of emails arriving at a server during any one hour period is known to be a Poisson random variable X with λ = β. The probability of an email being spam is p. What is the probability mass function, expected value, and variance of spam emails in a period of one hour?
The average number of passengers arriving at the Bus Station in Lancaster on Tuesday between 8:00...
The average number of passengers arriving at the Bus Station in Lancaster on Tuesday between 8:00 and 9:00 is 900. 1.To model this random phenomenon, which probability distribution is most suitable? Assume that passengers arrive at random at a constant rate throughout the hour. 2.Using the most suitable probability distribution, consider the following three statements: I. There are 15 passengers arriving every minute on average II. The standard deviation of the number of passengers arriving in an hour is 30...
Suppose that the mobile company central computer handles 60 million text messages a second. For each...
Suppose that the mobile company central computer handles 60 million text messages a second. For each text message it handles assume that there is an (independent) one in twelve million chance that it will be missed. What is the expected number of missed test messages in a second? What is the variance of the number of missed test messages in a second? What are the chances that the central computer misses exactly four test messages in the next second? (Use...
The number of people arriving for treatment at an emergency room can be modeled by a...
The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of five per hour. By using Poisson Distributions. Find: (i) What is the probability that exactly four arrivals occur during a particular hour? (ii) What is the probability that at least four people arrive during a particular hour? (iii) What is the probability that at least one person arrive during a particular minute? (iv) How many people do...
Consider the assumptions of a Poisson process given in class. Suppose the arrival of cars to...
Consider the assumptions of a Poisson process given in class. Suppose the arrival of cars to a restaurant follows a Poisson process. Which of the following examples do not violate an assumption of the Poisson process? two cars arrive at a restaurant at exactly the same time the probability of one car arriving between 9:10 and 9:20 is the same as the probability of one car arriving between 9:25 and 9:35 the probability of one car arriving between 9:04 and...
A grocery store counts the number of customers who arrive during an hour. The average over...
A grocery store counts the number of customers who arrive during an hour. The average over a year is 20 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals.     Find the probability that at least two customers arrive in a particular 4 minute period. Round your answer to four decimals.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT