Editing Probability Distributions (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Poisson Arrival' (Predicting how many customers will arrive in an hour):'''
<syntaxhighlight lang="python">
import math

def poisson_probability(avg_rate, k_events):
    """
    P(k) = (lambda^k * e^-lambda) / k!
    """
    p = ( (avg_rate**k_events) * math.exp(-avg_rate) ) / math.factorial(k_events)
    return round(p * 100, 2)

# Case: A coffee shop gets 5 people/hour on average. 
# What is the % chance of getting EXACTLY 10 people in one hour?
print(f"Chance of 10 people: {poisson_probability(5, 10)}%")
# What about exactly 5 (the average)?
print(f"Chance of 5 people: {poisson_probability(5, 5)}%")
</syntaxhighlight>

; Distribution Landmarks
: '''The Normal Distribution (Gauss)''' → The "God of Statistics." It describes almost everything in nature because nature is built from millions of tiny random forces adding up.
: '''The Pareto Principle (80/20 Rule)''' → A "Power Law" distribution: 80% of the effects come from 20% of the causes (e.g., 20% of words make up 80% of a book).
: '''The 'Black Swan' (Fat Tails)''' → Nassim Taleb's idea that we "Underestimate" the probability of "Extreme Events" (like stock market crashes) because we use the "Thin-tailed" Normal Distribution when we should be using "Fat-tailed" models.
: '''Bernoulli Trials''' — The simplest distribution: a single "Flip" with two outcomes (Success/Failure). It is the "Atom" of all probability.
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