Recall in lecture, the poisson distribution and binomial distribution converges

Question

Recall in lecture, the poisson distribution and binomial distribution converges when the number of trials is large and the probability of success is small. Write the MATLAB function poissonPMF.m (without using MATLAB’s built-in statistics functions). Your function should take n, lambda, and a vector x (representing a vector of integers [0, 1, 2, ... , n] where each value in this vector is evaluated) as input parameters and return a vector representing the pmf values for each value in x. Using your binomialPMF.m solution from Homework 2, comment on the following observations for both binomial and poisson distributions using the following parameters:

- n=10,p=0.5

- n=20,p=0.25

- n=30,p=0.1

- n=50,p=0.01

- n=100,p=0.001

Explanation / Answer

function res=calc_poisson(x,n,lambda)
res= (lambda^x)/((2.71828^lambda)*factorial(x))
end

function res_vec = calc_vec(vec)
sum=0.0
lambda=0.0
for i=1:length(vec)
sum=sum+vec(i)
end
lambda=sum/length(vec)
for i=1:length(vec)
res_vec(i)=calc_poisson(vec(i),size(vec),lambda)
end
end

calc_vec([1,2,3])

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