11.1 Why learn it ?

11.2 Introduction to Vectors(2-D, 3-D, n-D) , Row Vector and Column Vector

11.3 Dot Product and Angle between 2 Vectors

11.4 Projection and Unit Vector

11.5 Equation of a line (2-D), Plane(3-D) and Hyperplane (n-D), Plane Passing through origin, Normal to a Plane

11.6 Distance of a point from a Plane/Hyperplane, Half-Spaces

11.7 Equation of a Circle (2-D), Sphere (3-D) and Hypersphere (n-D)

11.8 Equation of an Ellipse (2-D), Ellipsoid (3-D) and Hyperellipsoid (n-D)

11.9 Square ,Rectangle

11.10 Hyper Cube, Hyper cuboid

11.11 Revision Questions

RevisionQuestions:

1. Define Point/Vector (2-D, 3-D, n-D)?

2. Howto calculate Dot productand angle between 2 vectors?

3. Define Projection, unit vector?

4. Equation ofaline(2-D), plane(3-D)and hyperplane(n-D)?

5. Distance ofa point froma plane/hyperplane, half-spaces?

6. Equation ofacircle(2-D), sphere(3-D)and hypersphere(n-D)?

7. Equation ofan ellipse(2-D),ellipsoid (3-D)and hyperellipsoid (n-D)?

8. Square, Rectangle, Hyper-cubeand Hyper-cuboid?

#Module 12 : Probability and Statistics
Section 12 is divided into sub sections

👉 12.1 Introduction to Probability and Statistics

👉 12.2 Population and Sample

👉 12.3 Gaussian/Normal Distribution and its PDF(Probability Density Function)

👉 12.4 CDF(Cumulative Distribution function) of Gaussian/Normal distribution

👉 12.5 Symmetric distribution, Skewness and Kurtosis

👉 12.6 Standard normal variate (Z) and standardization

👉 12.7 Kernel density estimation

👉 12.8 Sampling distribution & Central Limit theorem

👉 12.9 Q-Q plot:How to test if a random variable is normally distributed or not?

👉 12.10 How distributions are used?

👉 12.11 Chebyshev’s inequality

👉 12.12 Discrete and Continuous Uniform distributions

👉 12.13 How to randomly sample data points (Uniform Distribution)

👉 12.14 Bernoulli and Binomial Distribution

👉 12.15 Log Normal Distribution

👉 12.16 Power law distribution

👉 12.17 Box cox transform

👉 12.18 Applications of non-gaussian distributions?

👉 12.19 Co-variance

👉 12.20 Pearson Correlation Coefficient

👉 12.21 Spearman Rank Correlation Coefficient

👉 12.22 Correlation vs Causation

👉 12.23 How to use correlations?

👉 12.24 Confidence interval (C.I) Introduction

👉 12.25 Computing confidence interval given the underlying distribution

👉 12.26 C.I for mean of a random variable

👉 12.27 Confidence interval using bootstrapping

👉 12.28 Hypothesis testing methodology, Null-hypothesis, p-value

👉12.29 Hypothesis Testing Intution with coin toss example

👉 12.30 Resampling and permutation test

👉 12.31 K-S Test for similarity of two distributions

👉 12.32 Code Snippet K-S Test

👉 12.33 Hypothesis testing: another example

👉 12.34 Resampling and Permutation test: another example

👉 12.35 How to use hypothesis testing?

👉 12.36 Proportional Sampling

👉 12.37 Revision Questions

12.1 Introduction to Probability and statistics

12.2 Population and Sample

12.3 Gaussian/Normal Distribution and it's PDF ( Probability Density Function )

12.4 CDF ( Cumulative Distribution function ) of Gaussian/, Normal Distribution

12.5 Symmetric distribution, Skewness and Kurtosis

12.6 Standard normal variate (Z) and standardization

12.7 Kernel density estimation

12.8 Sampling distribution & Central Limit theorem