Lectured by Prof. Shun-Pin Hsu Ver. 091615 A first course in Probability (9 th ed.) A textbook of Sheldon Ross.

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Presentation transcript:

Lectured by Prof. Shun-Pin Hsu Ver A first course in Probability (9 th ed.) A textbook of Sheldon Ross

SPHsu's Probability Course/ch.1 2 General Approach and Mathematical Level

SPHsu's Probability Course/ch.1 3 Combinatorial Analysis Introductioin The basic principle of counting Permutations Combinations Multinomial Coefficients The number of integer solutions of equations

SPHsu's Probability Course/ch.1 4

Permutation n! is read as ‘n factorial’ ! SPHsu's Probability Course/ch.1 5

Permutationn SPHsu's Probability Course/ch.1 6

Combinations Attention ! SPHsu's Probability Course/ch.1 7

Combinations SPHsu's Probability Course/ch.1 8

Combinations SPHsu's Probability Course/ch.1 9

Combinations 1. Analytical proof (by induction) 2. Combinatorial proof Corollary: Easy but Important ! and SPHsu's Probability Course/ch.1 10

Combinations Q: What do we get as x 1 = x 2 =…= x r =1 ? SPHsu's Probability Course/ch.1 11

Combinations SPHsu's Probability Course/ch.1 12

Some useful identities SPHsu's Probability Course/ch (1.1) (1.2) Can you give combinatorial explanations for these identities ?

Some useful identities SPHsu's Probability Course/ch (2.1) (2.2) k n p (2.3) Can you give combinatorial explanations for these identities ? (2.5) (2.4)

Some useful identities SPHsu's Probability Course/ch.1 15 Can you give combinatorial explanations for these identities ?