In this lab, you'll practice your newly gained knowledge on the Bernoulli and Binomial Distribution.
You will be able to:
- Apply the formulas for the Binomial and Bernoulli distribution
- Apply NumPy to randomly generate Binomial and Bernoulli trials
- Use Matplotlib to generate Binomial and Bernoulli trials with various probabilities
When playing a game of bowling, what is the probability of throwing exactly 3 strikes in a game with 10 rounds? Assume that the probability of throwing a strike is 25% for each round. Use the formula for the Binomial distribution to get to the answer. You've created this before, so we provide you with the function for factorials again:
def factorial(n):
prod = 1
while n >= 1:
prod = prod * n
n = n - 1
return prod
p_3_strikes = None #answer = 0.2502822
0.25028228759765625
Now, create a function for the Binomial distribution with three arguments
def binom_distr(n,p,k):
None
Validate your previous result applying your new function.
# Your code here
0.25028228759765625
Now write a for loop along with your function to compute the probability that you have five strikes or more in one game. You'll want to use numpy here!
import numpy as np
# Your code here
Repeat the experiment 5000 times.
# leave the random seed here
np.random.seed(123)
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# the results should look like this:
# [0 1 2 3 4 5 6 7 8]
# [ 310 941 1368 1286 707 297 78 11 2]
[0 1 2 3 4 5 6 7 8]
[ 258 922 1475 1264 706 272 86 13 4]
Create the PMF using these empiric results (that is, the proportions based on the values we obtained running the experiment 5000 times).
import matplotlib.pyplot as plt
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You can see that, with a 25% strike hit rate, even when simulating 5000 times, an almost perfect and perfect game of 9 and 10 strikes didn't even occur once! If you change your seed, however, you'll see that occasionally perfect games will show up occasionally.
Next, let's create the CDF based on these results. You can use np.cumsum
to obtain cumulative probabilities.
# Your code here
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Congratulations! In this lab, you practiced your newly gained knowledge on the Bernoulli and Binomial Distribution.