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Statistical Sciences
Statistical Sciences 2244A/B
Jennifer Waugh

3-1 Overview ● Rare Even Rule for Inferential Statistics: if under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct 3-2 Fundamentals ● An event is any collection of results or outcomes of a procedure ● Asimple event is an outcome or an event that cannot be further broken down into simpler components ● The sample space for a procedure consists of all possible simple events. That is, the sample space consists of all outcomes that cannot be broken down any further ● Notation for Probabilities: ○ P denotes a probability ○ A, B, and C denote specific events ○ P(A) denotes probability of eventAoccurring ● Relative FrequencyApproximation of Probability: ○ P(A) = number of times A occurred / number of time trial was repeated ○ When finding probabilities with this, we obtain an approximation instead of an exact value; as total number of observations increases, approximation tends to get closer to actual probability ● ClassicalApproach to Probability (Requires Equally Likely Outcomes) ○ P(A) = number of ways Acan occur / number of different simple events ○ P(A) = s / n ● Subjective Probabilities: P(A), the probability of eventA, is estimated by using knowledge of relevant circumstances ● Law of Large Numbers: as a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability ● The mathematical probability of any event is 0, 1, or a number in between ○ probability of impossible events is 0 ○ probability of certain events is 1 ○ For any event, probability ofAis 0<= P(A) <= 1 Complementary Events ● The complement of eventA, denoted byAbar, consists of all outcomes in which eventA does not occur 3-3 Addition Rule ● P(Aor B) is the probability that either eventAoccurs or event B occurs, or they both occur ○ the word ‘or’in these cases is used inclusively which mean either one or the other or both ● Acompound event is any event combining two or more simple events ● When finding probability that eventAoccurs, or event B occurs, find the total number of ways Acan occur, and the number of ways B can occur, but find that total in such a way that no outcome is counted more than once ● FormalAddition Rule: P(Aor B) = P(A) + P(B) - P(Aand B) ● IntuitiveAddition Rule: To find P(Aor B), find the sum of the number of ways eventA can occur and the number of ways B can occur, adding in such a way that
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