Formula Sheet for STAT 100A Final - Permutations: - Combinations: - Binomial Theorem: - Famous Identity: - - Multinomial: - - Complementation Law: )(1)( APAPC - Addition Law: )()()()( BAPBPAPBAP - Conditional Probability: )()()|(BPBAPBAP - If events A and B are Independent then - If events A and B are Disjoint (Mutually Exclusive) then - De Morgan Laws: - Study the Generalized De Morgan' Laws and their proofs (more than two sets use induction). - Expectation or Expected Value or Mean:xxxPXE )()( - Variance: xxPxXEWhereXEXE )()(,)(222222 - Standard Deviation:2 - Bayes Theorem:Continuous Random Variables: Continuous Random Variables: Uniform Distribution: Gamma Distribution: Exponential Distribution: Chi-Squared Distribution:X~ Beta Distribution: For a geometric sequence with first term a1 = a and common ratio r, the sum of the first n terms is given
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