Dice & German Tank Problem

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
import seaborn as sns
import empiricaldist
from empiricaldist import Pmf, Distribution

Manual Way

dice = Pmf.from_seq([4,6,8,12])
dice

	probs
4	0.25
6	0.25
8	0.25
12	0.25

dice[4] *= 0
dice[6] *= 1/6
dice[8] *= 1/8 
dice[12] *= 1/12

dice.normalize()

0.09374999999999999

dice

	probs
4	0.000000
6	0.444444
8	0.333333
12	0.222222

def likelihood_dice(data, hypo):
    if data > hypo:
        return 0
    else:
        return 1 /hypo
    
    # Solution
    
# def likelihood_dice(data, hypo):
#     """Likelihood function for the dice problem.
    
#     data: outcome of the die roll
#     hypo: number of sides
    
#     returns: float probability
#     """
#     if data > hypo:
#         return 0
#     else:
#         return 1 / hypo

dice = Pmf.from_seq([4,6,8,12])
dice.update(likelihood_dice, 6)
dice

	probs
4	0.000000
6	0.444444
8	0.333333
12	0.222222

for roll in [8,7,7,5, 4]:
    dice.update(likelihood_dice, roll)

dice

	probs
4	0.000000
6	0.000000
8	0.919294
12	0.080706

dice.update??