ISI Kolkata - Statistics Assignment 3 - Problem 9

main.py

# Question 9
#
# Suppose X1 and X2 are IID from the discrete uniform distribution on
# {1, 2, ... , 5}. Derive the sampling distribution of (X1 + X2)/2. Verify
# your result by means of simulation.

from random import randint

# number of trials, more the trials accuracy increases
TRIALS = 10000000


def sample(a, b):
    return float(X1 + X2)/float(2)


# dictionary to record the frequency of sample result during each trial
count = {}

# executing trials
for _ in range(TRIALS):
    # Since X1 and X2 are independent and identically distributed from
    # the discrete uniform distribution on {1, 2, .., 5}.
    X1 = randint(1, 5)
    X2 = randint(1, 5)
    result = sample(X1, X2)
    # incrementing the count in the dictionary
    if result not in count.keys():
        count[result] = 0
    count[result] = count[result] + 1

# printing results
for key in sorted(count):
    print "%s: %s" % (key, count[key])

# results for 1,00,00,000 trials
# 1.0: 400795
# 1.5: 801592
# 2.0: 1199602
# 2.5: 1599320
# 3.0: 1997694
# 3.5: 1601549
# 4.0: 1198943
# 4.5: 798757
# 5.0: 401748