Question

PYTHON:

Using the function random.random_sample from numpy package write two functions:

* poissonRV(seed, mean,n) that returns for given seed a bunch of n Poisson distributed random numbers with the provided mean. You have to numerically calculate the inverse distribution function.

funnyDiceRV(seed,n) that returns for given seed a bunch of n random number which describe a biased die with distribution ℙ({1})=ℙ({2})=ℙ({3})=ℙ({4})=ℙ({5})=1/10P({1})=P({2})=P({3})=P({4})=P({5})=1/10 and ℙ({6})=1/2P({6})=1/2.

Answer 1

The Python code for generating Random numbers from the specified Poisson distribution and the specified Dice is given below:

from numpy import random
import math
def poissonRV(seed, mean,n):
        P = []
        limit = math.exp(-mean)
        random.seed(seed)
        for i in range(n):
             prod = random.random_sample(1)
             p  = 0
             while (prod >= limit):
                prod *= random.random_sample(1)
                p += 1
             P.append(p)
        return(P)
def funnyDiceRV(seed,n):
        D = []
        random.seed(seed)
        for i in range(n):
             r = random.random_sample(1)
             if(r<0.5):
                 r1 = random.random_sample(1)
                 if(r1<0.2):
                    D.append(1)
                 elif(0.2<=r1 and r1<0.4):
                    D.append(2)
                 elif(0.4<=r1 and r1<0.6):
                    D.append(3)
                 elif(0.6<=r1 and r1<0.8):
                    D.append(4)
                 elif(0.8<=r1 and r1<1):
                    D.append(5)
             else:
                 D.append(6)
        return(D)
P = poissonRV(10900, 100,5)
print("The Poisson RVs are : ", P)
D = funnyDiceRV(900, 12)
print("The Outcomes of the Dice are : ", D)

Sample output:

The Poisson RVs are : [94, 99, 104, 107, 79]
The Outcomes of the Dice are : [2, 6, 2, 6, 1, 2, 6, 6, 3, 2, 6, 5]