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Mgmt Sci Ch 3
Exam 1
47
Business
Undergraduate 4
09/14/2010

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Term

·         Experiment

Definition

o    The act of gathering data through observation

Term

·         Outcome

Definition

o    The result of an experiment

Term

·         Sample space

Definition

o    The collection of all possible outcomes of an experiment

Term

·         Probability

Definition

o    The likelihood that an outcome occurs

o    Two basic governing facts:

§  Probability associated with an outcome must be between 0 and 1

§  The sum of the probabilities over all possible outcomes must be 1.0

Term

·         Event

Definition

o    A collection one or more outcomes from a sample space

Term

·         Mutually exclusive

Definition

o    Both cannot occur that the same time

Term

·         Random variable

Definition

o    Numerical description of the outcome of an experiment

Function that assigns a real number toe each element of sample space

Term

·         Discrete random variable

Definition

o    The number of possible outcomes can be counted

Term

·         Continuous random variable

Definition

o    Outcomes over a continuous range of real numbers

Term

·         Probability distribution

Definition

o    Characterization of the possible values that a random variable may assume along with the probability of assuming these values

Term

·         Empirical probability distribution

Definition

o    An approximation of the probability distribution of the associated random variable

o    A theoretical model of the random variable

Term

·         Probability mass function

Definition

o    The probability distribution of the discrete outcomes

Term

·         Cumulative distribution function. F(x)

Definition

o    Specifies the probability that the random variable X will assume a value less than, or equal to a specified value, x

Term

·         Probability density function

Definition

o    Characterizes the outcomes of a continuous random variable

Term

·         Shape parameter

Definition

o    Controls the basic shape of the distribution

Term

·         Scale parameter

Definition

o    Controls the unit of measurement within the range of the distribution

Term

·         Location parameter

Definition

o    Specifies the location of the distribution relative to zero on the horizontal axis

Term

·         Expected value

Definition

o     (of a random variable) corresponds to the notion of the mean, or average, for a sample

Term

·         Bernoulli distribution

Definition

o    Characterizes a random variable with two possible outcomes with constant probabilities of occurrence               

Term

·         Binomial distribution

Definition

o    Models n independent replications of a Bernoulli experiment, each with a probability of p success

Term

·         Poisson distribution

Definition

o    A discrete distribution used to model the number of occurrences in some unite of measure

o    Ex. The # of events occurring in an interval of time, # of items demanded per customer from an inventory

Term

·         Uniform distribution

Definition

o    Characterizes a continuous random variable for which all outcomes between some min value a and max value b are equally likely

Term

·         Discrete uniform distribution

Definition

o    A variation of the uniform distribution

The random variable is restricted to be integer values between a and b (also integers)

Term

·         Normal distribution

Definition

o    A continuous distribution

o    Bell-shaped curve

Term

·         Standard normal distribution

Definition

o    The normal distribution with m = 0 and s2 = 1

Term

·         Triangular distribution

Definition

o    Continuous distribution defined by 3 parameters: the min, a; max, b; and most likely, c.

Term

·         Exponential distribution

Definition

o    Continuous distribution that models the time between randomly occurring events

Term
lognormal distribution
Definition
if the natural logarithm of a random variable X is normal, the X has a lognormal distribution
Term
gamma distribution
Definition
a family of distribution defined by a shape parameter, scale paramter, and location parameter
Term
Weibull Distribution
Definition
capable of taking on a number of different shapes defined ny a scale and shape parameter
Term
beta distribution
Definition

over a fixed interval from 0 to a positive valua s is the beta

 

a function of 2 shape parameters (both positive)

Term
geometric distribution
Definition
describes the number of trials until the first success where the probability of a succes is the same from trial to trial
Term
negative binomial distribution
Definition
models the distribution of the # of trials unteril the rth success
Term
hypergeometric distribution
Definition

applies to sampling w/o replacement

 

Term
logistics distribution
Definition
commonly used to describe growth of a population over time
Term
pareto distribution
Definition
describe the phenomena in which a small proportion of items accounts for a large proportion of some characteristics
Term
extreme value distribution
Definition

describes the largest value of responses over a period of tome

ec. rainfaill, earthquakes

Term
joint probability distribution
Definition
specifies the outcome of two different variables that occur at the same time, or jointly
Term
marginal probabilities
Definition
represent the probability associated with the outcomes of each random variable regardless of the value of the other
Term
conditional probability
Definition
the probability of occurrence of one vent A, given that anohter event B is known to have occurred
Term
statistically independent
Definition
one variable does not depend on thevalue of the other
Term
Monte Carloe Methocs
Definition
invlove sampling experiments whose purpose is to estimate the distribution of an outcome variable that depends on several input rando variables
Term
random number
Definition
defined as one that is uniformly distributed b/t 0 and 1
Term
random variate
Definition
a value ramdomly generated from a specified probability distribution
Term
sampling distribution of the mean
Definition
the means of multiple samples of a fixed size n from some population will form a distribution
Term
Νstandard error of the mean
Definition

the standard deviation of the sampling distribution of the mean

 

Term
central limit theorem
Definition
states that if the sample size is large enough, the sampling distribution of the mean can be approximated by a normal distribution, regardless of the shape of teh population distribution
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