Probability Theory 01

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Integral Calculus

1. To understand the Integration
2. The principle of the calculus: Newton-Leibniz Formula

Probability Space

1. Stochastic Variable & Probability: Probability Density Function
2. Stochastic Variable & Probability: Probability Space
3. Conditional Probability & Bayes Formula
4. Common Distribution & Conjugate Distribution

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Riemann Integra(Single Variable)

Concept:

1. Derivative: Make something very very very small.
2. Integral:
   • Algebra: An integral is analogous to a summation.
   • Geometry: The main function is to calculate the are of irregular shape.

Tips: To a certain extent, they are Inverse Operation(Derivative & Integral).

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Summary(Multivariate Integral Calculus)

• The meaning of algebra integral is infinite summation & The meaning of the geometry integral is calculate the volume without the sign.
• To a certain extent(For Indefinite Integral), Derivative & Integral are Inverse Operaion.(Such as +,- or x,/).
• If you are familiar with the Derivative, it will help you control the Integral.
• You can ragard the Multivariate Integral calculus as the sequence of Single Integral Calculus.

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The Man Who Knew Infinity – Srinivasa Ramanujan