Poisson distribution Definition and 127 Threads

A store opens at 8 in the morning. from 8 until 10 customers arrive at poisson rate 6 per hour. Between 10 and 12 they arrive at a poisson rate of 10 per hour. From 12 to 2, the store closes for lunch, Finally from 2 to 5 the arrival rate drops linearly from 10 per hour at 2 to four per hour at...

(Not sure if I should have posted this in the h/w problem section since it's not really hw...just a problem I've faced recently. But if it should be there, I can move it there. ) There are 5 boxes. Each box may contain a certain amount of marbles (1, 2, 3 etc.) and some have no marbles at...

I need to fit a Poisson distribution to this set of data (no. of counts of radioactive decay) The number of counts in a fixed time interval was recorded 500 times. With the number of counts going from 0 - 9 respectively 39 106 130 100 67 34 15 7 1 1 I understand how to use...

Please help with this thanks :) 1. (a) Define the Poisson probability distribution with mean μ. (b) Write down the binomial distribution for x successes in n independent trials each with probability p of success. (c) On average, 0.15% of the nails manufactured at a factory are known to...

Homework Statement A source of liquid is known to contain bacteria, with the mean number of bacteria per cubic centimeter equal to 3. Ten 1 c.c. test tubes are filled with liquid. Calculate the probability that all 10 test tubes will show growth, that is contain at least 1 bacterium each. (use...

b]1. Homework Statement [/b] prove that \sum( (e^(-u)) (u(^(x)) )/x! (from x=o to n ) = \int ( (e^(-y))(y^n) )dy/n! (from u to infinite ) Homework Equations The Attempt at a Solution i know that the left is Poisson distribution formula but how to do with the 'sum' ? and...

Homework Statement Let N,X1, X2, ... be independant random bariables where ?N has a poission Distribution with mean 3 while X1, X2... each has a poisson distribution with mean 7 Determine E[N \sum^N_{i=1} X_i] Homework Equations The Attempt at a Solution E[N \sum^N_{i=1} X_i]...

Homework Statement In a Poisson process with intensity λ, let X1 be the time until the first event and let X2 be the time between the first and the second event. Let Y be the time until the second event, that is, Y = X1 + X2. Find the density function f(y). 2. The attempt at a solution...

Homework Statement An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. If the number of claims filed has a Poisson distribution, what is the variance of the number of claims filed? [b]2. Homework Equations [/]...

Homework Statement Suppose a typographical errors committed by a typesetter occurs randomly. If that a book of 600 pages contains 600 such errors, calculate the probability by using Poisson's distribution. i) that a page contains no errors ii) that a page contains at least three errors...

Homework Statement The number of customers entering a cafe during tea time is known to be poisson distribution with λ = 5. on a particular day, given that at least 2 customers have entered the cafe during the tea time. what is the probability that at least 1 more customers will enter the cafe...

[SOLVED] Poisson Distribution Homework Statement Let X be the number of people entering the ICU in a hospital. From Historical data, we know the average number of people entering ICU on any given day is 5 a) What is the probability that the number of people entering the ICU on any given...

Homework Statement It rains on 10.3 days in the town in October on average. Let X denote the number of days in October on which it rains. Assume that rain falling on different days can be treated as independent events. (31 days in October). Write down an expression for the probability that it...

Homework Statement Suppose X has a Poisson distribution with parameter lambda. Given a random sample of n observations, Find the MLE of lambda, and hat lambda. Find the expected value and variance of hat lambda. Show that hat lambda is a consistent estimator of lambda. Homework...

Homework Statement Phone calls are received at Diane residence have a Poisson distribution with \lambda =2. a) If Diane takes a shower for 10 min, what is the probability that the phone rings Once or Twice. b) How long can she shower if the probability of receiving no calls be at most 0.5...

[SOLVED] A Chebyshev interval with a poisson distribution Geophysicists determine the age of a zircon by counting the number of uranium fission tracks on a polished surface; the number of these uranium fission tracks on this surface follows a Possion distribution. A particular zircon is of...

Doing Physics at University and I have never done poisson distributions. How the hell do I do it? The question is... Show that the data on the number of cavalry deaths in the Prussian Army in the 19th Century are consistent with the poisson probability distribution. The date were accumulated...

Can someone help me with this question: If X has a Poisson distribution so that 3P(X=1)=P(X=2) find the pdf of X, and P(X=4)?

Ok, If the mean time between a single random event occurring is 6 months then is the most probably month for the third event to occur the 18th month? Thanks!

Hi, in a Poisson Distribution test, what happens when the amount of time is doubled? For example, in 1 month, lamda=np and I can calculate the probability of x events happening in that 1month. However, if the question is changed to 6 months, what will i have to do? Thanks.

Hey, I want to write a Computer Simulation in C++, which simulates the development of a DNA sequence with a probability to mutate x in one "generation". I do have a variable number (=n) of copies of this DNA. Now one might think, to simulate the mutation by simply: sum(n*Poisson distributed...

Hello I'm Presented with the following Poisson distribution question P(X = x) = \frac{e^{-\lambda} \cdot \lambda^{x}}{x!} where x \in (1,2,3,\ldots) and \lambda > 0 Then I'm suppose to show that the above can be re-written if P(X \leq 1) = 1 - e^{- \lambda} Any idears on how I...

Could anybody attempt to solve this probability question? It incorporates the Poisson Distribution. Thank You. A company finds that it issues a mean of 7 pairs of earplugs a week to any employee. What is the probability that the number of pairs taken by any employee is 9 per week? (Using the...

so flaws in metal produced by high temperatures occur at a rate of 1 per 10 square feet. what is the probability that there is 3 or more flaws in a 8 x 5 feet. ok, so I know we need to use poisson disstribution on this, e^-np * np^k/k!. howver, I don't know my np. so 1 per 10 square...

ok, so on average, there is a chromosome mutation link once every 10,000 baby births. approximate the probability that exactly 3 of the next 20,000 babies born will have the mutation. so using poisson distribution, I let p = 1/10,000 n = 20,000. and use formula (e^(-np) * (np)^k /...

Hello In my text the following question is posed: ON a city street, car backfires are heard 8 times per hour. Use the poisson distribution to find an exact expression for the prob. that a car backfire is heard at most once in a given hour. Do not simplify or evaluate your answer. Now...

If you have a lottery (Megamillions) and you sell 20,000,000 tickets, the probability of them all losing is given by: (135,145,919/135,145,920)^20,000,000 = 0.862448363 A close approximation is given by: e^-(20,000,000/135,145,920) = 0.8624413 I just learned this from a book. That's...