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Lecture 2

Week 2 Lab notes.pdf

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Joe Campolieti

MA240 Lab Notes - Week 2 Text Reference: 1.1-1.3 On Frequencies and Histograms (1.1) ▯ Frequency -the number of times a certain outcome occurs in a ▯nite number of repetitions of a random experiment ▯ Relative Frequency - the ratio of the frequency of an outcome divided by the number of times the experiment is repeated ,! Probability Interpretation: The probability of a random event is the relative frequency of the outcome when repeating the experiment many times ▯ Histogram - a graphical representation of the data tallied from a frequency table ,! helps us easily determine the mode of a data set ▯ Mode is the observation which occurs with the greatest frequency ▯ Probability Mass Function (p.m.f.): function that describes the probabilities of all outcomes of a random experiment Properties of Probability (1.2) ▯ Algebra of Sets: (Review) (a) ; ! The null/empty set. :No elements in the set (b) A ▯ B !The set A is a subset of the set B. All elements in the set A are also part of the set B (c) A [ B ! Union of the sets A and B. Denotes all the elements that are a part of set A OR set B. (d) A \ B ! Intersection of the sets A and B. Denotes all elements that are a part of both A AND B. 0 (e) A ! The complement of A. All elements that are in the Universal space S that are NOT in A. ▯ Frequency Interpretation: If n [▯nite] equally likely possibilities [events/outcomes], of which one must occur and s are considered "successes" [i.e., satisfy the conditions of a speci▯ed event, E], then the probability of a s success is given by P (E) = n ,! the probability of an event is the proportion of times the event would occur over a long run of repeated experiments ,! Example: rolling a fair die...repeated rolls will show that a 1 will appear 1 out of 6 times - so the probability 1 is 6 ▯ Mutually exclusive events: have no elements in common; i.e., A \ B = ? ,! therefore, P (A \ B) = 0 for mutually exclusive events A and B ▯ Exhaustive events : all the elements in the space are in the union, i.e., A [ B [ C = S (universal set)
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