# An ordered subset is called a permutation p kn an

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An ordered subset is called a permutation, P k,n 𝑛! (𝑛−𝑥)! An unordered subset is called a combination. We denote C k,n or ( 𝑛 𝑘 ) read” n choose k” = 𝑛! 𝑥!(𝑛−𝑥)! Conditional probability: P(A|B) = 𝑃(?∩?) 𝑃(?) Law of Total Probability: 𝑃(?) = 𝑃(?|? 1 )𝑃((? 1 ) + ⋯ + 𝑃(?|? 𝑘 )𝑃(? 𝑘 ) where ? 𝑖 ′? are disjoint events and ? 𝑘 𝑖=1 𝑖 = 𝑆 Bayes theorem/rule= 𝑃(? 𝑖 |?) = 𝑃(? 𝑖 ∩?) 𝑃 ( ? | ? 1 ) 𝑃((? 1 )+⋯+𝑃(?|? 𝑘 )𝑃(? 𝑘 ) Independence: P(A|B) = P(A) Multiplicative rule: P (A B) = P(A) · P(B) if and only if A and B are independent. Chapter 3: Random Variable (rv) Types of rv: Discrete and continuous Bernoulli variable: Any random variable whose only possible values are 0 and 1 Probability Distributions: the distribution of a rv x, P(X=x)/f(x) is a probability distribution if 0 f(x) 1 and ∑ ?(?) = 1 Pmf and pdf Expected Values: E(X)= ∑ ??(?) Var(x)= ∑(? − ?̅) 2 ?(?) = E(X 2 )-[E(X)] 2 Standard deviation of x, 𝜎 𝑥 = √?𝑎?(?) ?? √𝜎 2 Parameter(s) of a distribution completely specifies the distribution. The Binomial Probability Distribution: Bin (n, p) The pmf of binomial distribution is P(x=x) or f(x)= { ( 𝑛 𝑥 )? 𝑥 (1 − ?) 𝑛−𝑥 for x = 0,1,2, 3. . . n 0 ??ℎ???𝑖?? Hypergeometric, Hyp (N, n, M) Negative Binomial Distributions NB (r, p) The Poisson Distribution, Pois( 𝜇 ) The pmf of Poisson distribution is P(x=x) or f(x)= { 𝑒 −𝜇 𝜇 𝑥 𝑥! ??? ? = 0,1,2,3 … 0 ??ℎ???𝑖?? Poison can be used as a limiting form of Binomial distribution if n>50 and np<5.

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• Fall '19
• Probability theory, Binomial distribution, Discrete probability distribution, AUB

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