Stats Exam 2

probability theory
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Terms in this set (25)
probability theory
the science of uncertainty or chance. It is the likelihood that a certain event will occur.
Equal-Likelihood Model
every possible sample from the total number of possible outcomes is equally likely to be chosen.
Basic Properties of Probabilities
Property 1: The probability of an event is always between 0 and 1,
inclusive.
Property 2: The probability of an event that cannot occur is 0. (An
event that cannot occur is called an impossible event.
Property 3: The probability of an event that must occur is 1. (An
event that must occur is called a certain event.
Frequentist interpretation of probability
construes that the probability of an event to be proportion of times it occurs in a large number of repetitions of the experiment.
The Complementation Rule
P(E) = 1 - P(EC)
mutually exclusive events
two or more events that can not occur together
dependent events
Is when one event having occurred changes the probability of a second event occurring.
conditional probability
the probability of an event occurring given that another event has already occurred.
contingency tables
A contingency table is a table for bivariate data. It can be used to show the joint probabilities such as Pr( A and B ) and the conditional probabilities such as Pr( A|B ) or Pr( B|A )
density curve
a smooth curve representing a frequency distribution.
density scalethe plot of the vertical coordinates on the density curve. If the density scale is used, then the relative frequencies are represented as areas under the curverandom variablevariable that takes on numerical values that depend on the outcomes of a chance operation.binomial coefficientIf n is a positive integer and j is a nonnegative integer less than or equal to n , then the binomial coefficient is nC jBernoulli trialsare repeated identical trials. The trials are called this type of trial if certain criteria are met 1. n is the number of trials 2. Each trial has two possible outcomes - success and failure 3. The probability of a success p remains the same from trial to trial 4. The trials are independentbinomial distributionthe probability distribution for the number of successes in a sequence of Bernoulli trials.normal curvedistribution represented by a normal curve.standardized normal distribution/curveA normally distributed variable having mean 0 and standard deviation 1basic properties of the standard normal curveProperty 1: The total area under the standard normal curve is 1. Property 2: The standard normal curve extends indefinitely in both directions, approaching but never touching, the horizontal axis as it does so. Property 3: The standard normal curve is symmetric about 0; that is, the part of the curve to the left of the dashed line is the mirror image of the part of the curve to the right of it. Property 4: Almost all the area under the standard normal curve lies between -3 and 3.Z sub alpha notationThe symbol Zα is used to denote the z-score that has an area of α (alpha) to its right under the standard normal curve. It is read as "Zα" as "z sub α" or more simply as "z α"Empirical Rule68.25% of all possible observations lie within one standard deviation to either side of the mean 95.44% of all possible observations lie within two standard deviations to either side of the mean 99.74% of all possible observations lie within three standard deviations to either side of the meannormal probability plotplot where the ranked observed values are plotted against the normal scoresnormal scoresthe data points that we would expect to obtain if our data was following a standard normal distributionsampling errorerror resulting from using a sample to estimate a population characteristic.sampling distribution of a statisticdistribution of the statistic, that is given the distribution of all of the possible observations of the statistic for samples of a given size from a populationmeta experimentsexperiments where every possible sample that can be taken from a population is taken.