Probability Basics

Simulazione statistica in Python

Tushar Shanker

Data Scientist

Sample Space

Sample Space $S$: Set of all possible outcomes

Dice Sample Space

Simulazione statistica in Python

Probability

Sample Space $S$: Set of all possible outcomes

Probability $P(A)$: Likelihood of event $A$

  • $0 \leq P(A) \leq 1$
  • $P(S) = 1$ eg. $P(H) + P(T)=1$
Simulazione statistica in Python

Probability

Sample Space $S$: Set of all possible outcomes

Probability $P(A)$: Likelihood of event $A$

  • $0 \leq P(A) \leq 1$
  • $P(S) = 1$ eg. $P(H) + P(T)=1$

Coin

Simulazione statistica in Python

Mutually Exclusive Events

Sample Space $S$: Set of all possible outcomes

Probability $P(A)$: Likelihood of event $A$

  • $0 \leq P(A) \leq 1$
  • $P(S) = 1$
    • $P(H) + P(T)=1$
  • For mutually exclusive events $A$ and $B$:
    • $P(A \cap B) = 0$
    • $P(A \cup B) = P(A) + P(B)$
Simulazione statistica in Python

Probability

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

A Intersection B

Simulazione statistica in Python

Using Simulation for Probability Estimation

Steps for Estimating Probability:

  1. Construct sample space or population.
  2. Determine how to simulate one outcome.
  3. Determine rule for success.
  4. Sample repeatedly and count successes.
  5. Calculate frequency of successes as an estimate of probability.
Simulazione statistica in Python

Let's practice!

Simulazione statistica in Python

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