Stats Distribution: Solving CW Question on Poisson Distribution

In summary, the given question deals with the number of wrecks in a specific area of sea with a Poisson distribution and a known probability of a wreck being known. The task is to find the conditional distribution of known wrecks given the total number of wrecks, as well as the marginal distribution of known wrecks. This can be solved using the binomial distribution and the joint probability function.
  • #1
01jbell
6
0
hey guys/gals i have been given this cw question however i spent ages and can't seem to get my head around it can some one give me a hand

" the number N of wrecks in a particular area of sea off the Cornish coast has a poisson distribution with mean [tex]\propto[/tex] . the probability that a wreck is known is p . Let X denote the number of known wrecks

(a) state the conditional distribution of X given N=n

(b) Find the Marginal Distribution of X "

thats the question now i think (a) has some hting to do with Binonial distribution

but i am complety stummped on (b)

any help would be great

thanks
 
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  • #2
I would start by writing out the binomial distribution for
P(X=x|N=n)

the form for P(N=n) is also given

if i remember right, the joint pdf can be given to be
P(X=x, N=n) = P(X=x|N=n)P(N=n)

from that you should be able to find the marginal distribution by summing over n
 

What is a Poisson distribution and when is it used?

A Poisson distribution is a type of probability distribution that is used to model the number of events that occur in a specific time interval or space, given a known average rate of occurrence. It is typically used when the events are independent and occur at a constant rate.

How is the Poisson distribution different from other distributions?

The Poisson distribution is different from other distributions in that it only has one parameter, the rate of occurrence, whereas other distributions may have multiple parameters. It also models the number of events that occur in a specific interval, rather than the probability of a specific value occurring.

How do you solve a CW question on Poisson distribution?

The first step in solving a CW question on Poisson distribution is to identify the average rate of occurrence (λ). Then, use the Poisson formula (P(x) = e^-λ * λ^x / x!) to calculate the probability of the given number of events (x) occurring. Finally, use the appropriate tables or a calculator to find the solution.

What is the importance of understanding Poisson distribution in statistics?

Understanding Poisson distribution is important in statistics because it is commonly used to model real-world phenomena, such as the number of customers in a store or the number of calls received by a call center. It also has many applications in various fields, such as biology, economics, and engineering.

What are some potential limitations of using Poisson distribution?

One potential limitation of using Poisson distribution is that it assumes events occur independently of each other and at a constant rate, which may not always be the case in real-world scenarios. It also only models the number of events, rather than the values associated with those events. Additionally, Poisson distribution may not be appropriate for small sample sizes or when the average rate of occurrence is very low or high.

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