Generate a Poisson random variable

The problem I need to solve is as below:

To generate a Poisson random variable with parameter λ use the following:

X=min ∑Ui exp(-λ) ; i=1,2...n

where Ui are i.i.d samples from the uniform distribution.

Show that X is Poisson (λ). Plot them.

How to solve this?

[Image Analyst]

Have you tried a for loop:

for i = 1 : n

[ABUL HASNAT]

I have tried this way:

a=0;b=1;

ns =10000;% ns = sample size

S = zeros(ns,1);

Y = zeros(ns,1);

lambda = 4;

for i=1:ns; % starting loop

n = 0; %minimum n

U=a+(b-a)*rand;

while U>=exp(-lambda); % repeat if prod is less than or equal to exp(-lambda)

U=U*[a+(b-a)*rand];

n=n+1;

end

Y(i) = U;

S(i)=n;

bar(S);

end

xlabel('Sample size');ylabel('Poisson random variables');

But the output is not possion look alike. How can I prove it? Help.

Answer 1

[the cyclist]

Use

histogram(S)

instead of

bar(S)

and move that line out of the for loop, so you don't have to draw it 10,000 times. :-)