[solved] – Question 87850

One of the many methods of generating values ​​of a Poisson X random variable with parameter  is as follows.

1-Generate random variables Uniforms U1, U2, …

2-Let I be the smallest index such that
Π_ (i = 1) ^ (I + 1) ▒ 〖U_ (i) <e ^ (- λ)〗

3- Do X = I-1

Make a function in Python that simulates n Poisson values ​​with parameter  using the given method.
– The number of customers arriving at a restaurant car behaves like a Poisson variable with  = 25 per hour. Simulate the arrival process by time intervals of 5 minutes.
-Using the simulated data, estimate the mean and variance of the number of clients that arrive at the car service in a period of 10 minutes.
– Estimate the probability that more than 10 cars arrive in half an hour. Compare the estimate with the true result.
-If X is a Poisson with parameter . Generate 1000 values ​​of the variable Y = (X-) / 1 / 2 for  = 5,10,20,30,40 and 50 and make your histogram, what comments do you deserve?

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