AI Basics with AK

Season 03 - Introduction to Statistics

Arun Koundinya Parasa

Episode 06 - Probability Distributions

Re-Cap of Episode -05

Term	Meaning
Sample Space (S)	Set of all possible outcomes
Event (E)	A subset of the sample space
Outcome	A single result from the sample space

Probability of an Event

P(E) = Number of favorable outcomes / Total number of outcomes

Example: Probability of getting Heads when tossing a coin:

P(Heads) = 1/2 = 0.5

Single Trial -> Many Trials

• What if we roll many times? -> After enough rolls -> There is a pattern

What is a Probability Distribution?

A Probability Distribution shows how probabilities are assigned to all possible outcomes.

Types of Probability Distributions

Distribution Type	Description	Examples
Discrete Distributions	Finite/countable outcomes	Dice, Coin Flips
Continuous Distributions	Infinite outcomes over a range	Height, Weight

Types of Important Distributions

Distribution	Type	Example	Shape / Key Feature
Uniform	Discrete / Continuous	Rolling a die, random pick	All outcomes equally likely; flat histogram
Normal	Continuous	Heights, exam scores	Bell-shaped; most outcomes near the mean
Binomial	Discrete	Coin flips (count successes)	Counts of successes; hill-shaped at discrete points

Understanding Distribution Names

Distribution	Why It’s Called That	Key Idea
Uniform	“Uniform” means all the same	All outcomes equally likely -> flat histogram
Normal	Called “normal” because it’s the common pattern in nature	Most values cluster near the mean -> bell-shaped curve
Binomial	Comes from “bi” (two outcomes) and “nomial” (counting formula)	Counts successes/failures in repeated yes/no trials -> hill at discrete points

Key Takeaways:

• Uniform -> everything is equal (e.g., dice roll)
  
• Normal -> most things cluster around average (e.g., heights, scores)
  
• Binomial -> counting yes/no outcomes repeatedly (e.g., coin flips)

Visualizing Distributions

Thank You

Next episode, we dive into Central Limit Theorem