Statistics and Probability

Introduction

• Introduction to Dr. Gajinat Purohit.
• Topic: Statistics and Probability.
• This topic is slightly above the level of 12th grade for engineering and B.Sc. students.
• Students are advised to understand basic principles from the 12th-grade level.

Content Overview

• Main topics:
  • Probability
  • Random Variable

Random Variable

• Two types of random variables:
  1. Discrete Random Variable
  2. Continuous Random Variable

Discrete Random Variable

• Example: Toss of a coin.
• Sample Space:
  • Once: {Head, Tail}
  • Twice: {HH, HT, TH, TT}
• Probability Distribution:
  • Probability of 0 head: 1/4
  • Probability of 1 head: 1/2
  • Probability of 2 heads: 1/4

Continuous Random Variable

• Example: Weight of students at college.
• Sample Space: between 50 and 60.
• Every point is covered.

Probability Metrics

• PMF: Probability Mass Function
  • Properties:
    • P(X) ≥ 0
    • ΣP(X) = 1
• PDF: Probability Density Function
  • Properties:
    • ∫f(x)dx = 1
    • f(x) ≥ 0

Mathematical Expectation

• Mean, Variance, Moments
• Distributions:
  • Binomial
  • Poisson
  • Exponential
  • Normal
  • Uniform

Properties of Distributions

• Moments:
  • Moment about Mean
  • Moment about Origin
  • Moment about Any Other Point

Skewness and Kurtosis

• Symmetry of data
• Positively skewed, negatively skewed, or symmetric data.
• The study of the normal distribution curve.

Relation and Regression

• Probability Density Function
• Distribution Functions

Conclusion

• Thank you for watching the video.
• The discussion of all topics continues.
• Stay tuned!