lecture4 notes - LECTURE 4 Discrete uniform law Readings...

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LECTURE 4 Discrete uniform law Readings: Section 1.6 Let all sample points be equally likely Then, Lecture outline number of elements of A A P ( A ) = = | | total number of sample points Principles of counting | | Just count . . . Many examples permutations k -permutations combinations partitions Binomial probabilities Basic counting principle Example r stages Probability that six rolls of a six-sided die n i choices at stage i all give di ff erent numbers? Number of outcomes that make the event happen: Number of elements in the sample space: Number of choices is: n 1 n 2 · · · n r Answer: Number of license plates with 3 letters and 4 digits = . . . if repetition is prohibited = Permutations: Number of ways of ordering n elements is: Number of subsets of { 1 , . . . , n } = 1
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Combinations Binomial probabilities n : number of k -element subsets k n independent coin tosses of a given n -element set P ( H ) = p Two ways of constructing an ordered
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