More Probability Concepts

Statistical Simulation in Python

Tushar Shanker

Data Scientist

Conditional Probability

  • Conditional Probability
    • $P(A|B) = \dfrac{P(A \cap B)}{P(B)}$

A Intersection B

Statistical Simulation in Python

Conditional Probability

  • Conditional Probability

    • $P(A|B) = \dfrac{P(A \cap B)}{P(B)}$

    • $P(B|A) = \dfrac{P(B \cap A)}{P(A)}$

    • $P(A \cap B) = P(B \cap A)$

Statistical Simulation in Python

Bayes Rule

  • Conditional Probability

    • $P(A|B) = \dfrac{P(A \cap B)}{P(B)}$

    • Bayes' rule: $P(A|B) = \dfrac{P(B|A) P(A) }{P(B)}$

Statistical Simulation in Python

Independent Events

  • Independent Events

    • $P(A \cap B) = P(A)P(B)$

    • Conditional Probability: $P(A|B) = \dfrac{P(A \cap B)}{P(B)} = \dfrac{P(A)P(B)}{P(B)} = P(A)$

Statistical Simulation in Python

Solar Panels & Clean Vehicles

  • Number of houses = 150

Solar Panel Data

Statistical Simulation in Python

Solar Panels & Clean Vehicles

$P(\text{Solar}) = P(\text{Solar} \cap \text{Hybrid, EV}) + P(\text{Solar} \cap \text{No Hybrid, EV}) = \frac{30}{150} + \frac{10}{150}=\frac{40}{150}$

Solar Panel - Marginal Probabilities

Statistical Simulation in Python

Solar Panels & Clean Vehicles

$P(\text{Solar} | \text{Hybrid, EV}) = \dfrac{P(\text{Solar} \cap \text{Hybrid, EV})}{P(\text{Hybrid, EV})} = \frac{30}{80} = 0.375$

Solar Panel Conditional Probabilities

Statistical Simulation in Python

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Statistical Simulation in Python

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