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
,! 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
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.
(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
success is given by P (E) =
,! the probability of an event is the proportion of times the event would occur over a long run of repeated
,! Example: rolling a fair die...repeated rolls will show that a 1 will appear 1 out of 6 times - so the probability
▯ 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)