Probability Basics Tushar Shanker Data Scientist DataCamp - - PowerPoint PPT Presentation

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Probability Basics Tushar Shanker Data Scientist DataCamp - - PowerPoint PPT Presentation

Mar 15, 2023 267 likes •572 views

DataCamp Statistical Simulation in Python STATISTICAL SIMULATION IN PYTHON Probability Basics Tushar Shanker Data Scientist DataCamp Statistical Simulation in Python Sample Space Sample Space S : Set of all possible outcomes DataCamp

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DataCamp Statistical Simulation in Python

Probability Basics

STATISTICAL SIMULATION IN PYTHON

Tushar Shanker

Data Scientist

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DataCamp Statistical Simulation in Python

Sample Space

Sample Space S: Set of all possible outcomes

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DataCamp Statistical Simulation in Python

Probability

Sample Space S: Set of all possible outcomes Probability P(A): Likelihood of event A 0 ≤ P(A) ≤ 1 P(S) = 1 eg. P(H) + P(T) = 1

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DataCamp Statistical Simulation in Python

Probability

Sample Space S: Set of all possible outcomes Probability P(A): Likelihood of event A 0 ≤ P(A) ≤ 1 P(S) = 1 eg. P(H) + P(T) = 1

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DataCamp Statistical Simulation in Python

Mutually Exclusive Events

Sample Space S: Set of all possible outcomes Probability P(A): Likelihood of event A 0 ≤ P(A) ≤ 1 P(S) = 1 P(H) + P(T) = 1 For mutually exclusive events A and B: P(A ∩ B) = 0 P(A ∪ B) = P(A) + P(B)

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DataCamp Statistical Simulation in Python

Probability

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

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DataCamp Statistical Simulation 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.
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DataCamp Statistical Simulation in Python

Let's practice!

STATISTICAL SIMULATION IN PYTHON

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DataCamp Statistical Simulation in Python

More Probability Concepts

STATISTICAL SIMULATION IN PYTHON

Tushar Shanker

Data Scientist

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DataCamp Statistical Simulation in Python

Conditional Probability

Conditional Probability P(A∣B) = P(B) P(A ∩ B)

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DataCamp Statistical Simulation in Python

Conditional Probability

Conditional Probability P(A∣B) = P(B∣A) = P(A ∩ B) = P(B ∩ A) P(B) P(A ∩ B) P(A) P(B ∩ A)

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DataCamp Statistical Simulation in Python

Bayes Rule

Conditional Probability P(A∣B) = Bayes' rule: P(A∣B) = P(B) P(A ∩ B) P(B) P(B∣A)P(A)

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DataCamp Statistical Simulation in Python

Independent Events

Independent Events P(A ∩ B) = P(A)P(B) Conditional Probability: P(A∣B) = = = P(A) P(B) P(A ∩ B) P(B) P(A)P(B)

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DataCamp Statistical Simulation in Python

Solar Panels & Clean Vehicles

Number of houses = 150

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DataCamp Statistical Simulation in Python

Solar Panels & Clean Vehicles

P(Solar) = P(Solar ∩ Hybrid, EV) + P(Solar ∩ No Hybrid, EV) = + = 150 30 150 10 150 40

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DataCamp Statistical Simulation in Python

Solar Panels & Clean Vehicles

P(Solar∣Hybrid, EV) = = = 0.375 P(Hybrid, EV) P(Solar ∩ Hybrid, EV) 80 30

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DataCamp Statistical Simulation in Python

Let's practice!

STATISTICAL SIMULATION IN PYTHON

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DataCamp Statistical Simulation in Python

Data Generating Process

STATISTICAL SIMULATION IN PYTHON

Tushar Shanker

Data Scientist

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DataCamp Statistical Simulation in Python

Simulation Steps

  • 1. Define Possible Outcomes for Random Variables.
  • 2. Assign Probabilities.
  • 3. Define Relationships between Random Variables.
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DataCamp Statistical Simulation in Python

Data Generating Process

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DataCamp Statistical Simulation in Python

Cricket

source: Wikipedia

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DataCamp Statistical Simulation in Python

Cricket

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DataCamp Statistical Simulation in Python

Cricket

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DataCamp Statistical Simulation in Python

Let's practice!

STATISTICAL SIMULATION IN PYTHON

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DataCamp Statistical Simulation in Python

eCommerce Ad Simulation

STATISTICAL SIMULATION IN PYTHON

Tushar Shanker

Data Scientist

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DataCamp Statistical Simulation in Python

eCommerce Funnel

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DataCamp Statistical Simulation in Python

Signup Flow

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DataCamp Statistical Simulation in Python

Purchase Flow

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DataCamp Statistical Simulation in Python

Let's practice!

STATISTICAL SIMULATION IN PYTHON