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Electrical and Computer Engineering Department

EE353 Glossary

Experiment Any process that generates a set of data
Observation A recording of data, either numerical or by category
Sample space The set of all possible outcomes from a statistical experiment, usually designated by symbol S
Event A subset of a sample space S
Complement For an event A in sample space S, the complement is the set of all elements of S that are not in A
Null set A set or event with no elements
Intersection With regards to two events, the intersection is the set of all elements common to both events
Mutually exclusive When two events have no elements in common, they are mutually exclusive or disjoint
Union The union of two events is the set of all elements of either or both events
Venn diagram A visual representation of the relationships between a sample space and events in the sample space
Tree diagram A diagram with a structure of branching connecting lines, representing different processes and relationships
Permutation An arrangement of all or part of a set of objects, where their order is important
n-factorial (n!) The product of all integers from 1 up to and including n, where n is a positive integer. Note: by definition, 0! = 1
Cell A subset of a set of n objects
Partition When a set of n objects is divided into r cells, the cells intersection is Φ, and all n objects are accounted for
Combination Selections produced by choosing r objects from n objects without regard to their order; this produces 2 cells: one with n objects, one with n-r objects
Probability The likelihood of the occurrence of an event in a statistical experiment, which is assigned a number between 0 and 1
Conditional Probability The likelihood of the occurrence of an event B in a statistical experiment when it is known that event A has already occurred, written as P(B|A)
Independent Two events are independent if the fact that one occurred does not affect the probability that the other will occur: P(A|B)=P(A)
Random Variable A function that associates a real number with each element in the sample space
Discrete Sample Space A sample space with a finite # of possibilities, or with an unending sequence with as many elements as there are whole numbers (also called countably infinite)
Continuous Sample Space A sample space with an infinite # of possibilities, equal to the number of points on a line segment
Discrete Probability Distribution Function For a discrete random variable X, this is a set of ordered pairs (x,f(x)) such that f(x)>=0, the sum of f(x)=1, and P(X=x)=f(x). Also called probability mass function (pmf)
Discrete Cumulative Distribution Function (cdf) For a discrete probability function f(x), this is F(x), where F(x)=P(X≤x)=the sum of f(t), for tx
Probability Density Function (pdf) For a continuous random variable X, this is a function f(x) where f(x)≥0, the integral of f(x)=1, and P(a<x<b) = the integral of f(x) between a and b
Cumulative Distribution Function (cdf) For a continuous probability density function f(x), this is F(x), where F(x)=P(Xx)=integral of f(t), from -inf to t
Mean, or Expected Value of Random Variable X For a discrete probability function f(x), μ=E(X)=the sum of all x times f(x), or for continuous f(x), μ=E(X)=the integral of x times f(x) from –infinity to infinity.
Variance of Random Variable X A measure of the variability of a random variable, for example is the probability distribution of the values of x compact, or widely dispersed. For a discrete distribution, σ2=E[(X–μ)2]=the sum of all (x-μ)2 times f(x), or for continuous, is equal to the integral of (x-μ)2 times f(x) from –infinity to infinity. A simpler expression is that σ2=E(X2)–μ2.
Standard Deviation of Random Variable X The positive square root of the variance of X.
Deviation of an Observation The quantity x–μ. This is a measure of how far an observation is from the mean of the random variable.
Variance of Random Variable g(X) For a discrete distribution, σ2=E[(g(X)–μg(x))2]=the sum of all (g(x)-μg(x))2 times f(x), or for continuous, is equal to the integral of (g(x)-μg(x))2 times f(x) from –infinity to infinity. A simpler expression is that σ2=E(g(X)2)–μg(x)2.

 

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