STA257H1 Lecture Notes - Lecture 2: Sample Space, Mexican Peso, Binomial Theorem
Document Summary
Probability does not exceed 1: probability is non-negative, the probability of the union of dis oint events is the sum of, probability of the complement of a is 1 minus probability of their individual probabilities addition rule. Review of cardinality: prove for any probability rri^sure p that. , p ( 0 ) = o / t " ^ ^ ^ ^ ^ ^ /^ ^ ^ ^^ Exercise: a, sample spaces with distinct sample points are called discrete: sample space: finite # of elements. Roll of a die, toss of a coin infinite sample space: countably. Countably infinite # of elements (elements can be put into a one-to-one correspondence with natural numbers. Number of coin tosses before first head appears: consider d={1,2,3,} (countably infinite) Let p{i) = measure? for 7 = 1,2,3,; is p a probability oacf}> &ic. Cannot have^ountably mfjnite s a n i p l e ^ p a c^ with equiprobable sample points. ywiyty in/inite ^ infinit.
