Introduction to Statistics by Ewa Paszek - HTML preview

χ2 4.07χ2 χ 2 test (k. pearson, 1900),

, Gamma Distribution, Chi-Square Distribution, NORMAL DISTRIBUTION, Glossary, Properties of Estimators, CONFIDENCE INTERVALS I, Glossary, , , Glossary

a bar graph,

a bernoulli distribution, Bernoulli distribution

a bernoulli experiment, BERNOULLI TRIALS AND THE BINOMIAL DISTRIBUTION

a best critical region of size simplemath mathml-miitalicsα 1.19.510000000000002pt8.51pt0 0 9.510000000000002 8.512.1099999999999994none#000000optimizeLegibilitySTIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariantsfont-family: STIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariants; fill: ; background-color: transparent; font-family: STIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariants; fill: ; background-color: transparent; font-family: STIXGeneral, STIXSizeOneSym, STIXIntegralsD, STIXIntegralsSm, STIXIntegralsUp, STIXIntegralsUpD, STIXIntegralsUpSm, STIXNonUnicode, STIXSizeFiveSym, STIXSizeFourSym, STIXSizeThreeSym, STIXSizeTwoSym, STIXVariants; font-style: italic; fill: black; background-color: transparent; 26.410α α , Glossary

a best critical region of size α 2.1099999999999994α α ,

a binomial distribution,

a confidence interval, CONFIDENCE INTERVALS I, Glossary

a cycle,

a discrete sample space,

a distribution of the discrete type,

a gamma distribution, SUMMARIZING

a geometric distribution,

a linear, Proof

a measure of the dispersion or spread of a distribution is defined as follows:,

a most powerful test,

a multiplicative congruential generator,

a poisson distribution, , Glossary

a prime-modulus multiplicative congruential generator,

a probability histogram,

a procedure called parameter estimation, which assesses goodness of fit, ESTIMATION

a random variable, RANDOM VARIABLE OF DISCRETE TYPE, Glossary

a random variable of the discrete type,

a set of discrete points,

a shuffled generator, Combinations of Generators (Shuffling)

a simple hypothesis,

a simple null hypothesis,

a test of a statistical hypothesis,

a uniform distribution, The Uniform Distribution, Glossary

a uniformly most powerful critical region of size simplemath mathml-miitalicsα 1.19.510000000000002pt8.51pt0 0 9.510000000000002 8.512.1099999999999994none#000000optimizeLegibilitySTIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariantsfont-family: STIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariants; fill: ; background-color: transparent; font-family: STIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariants; fill: ; background-color: transparent; font-family: STIXGeneral, STIXSizeOneSym, STIXIntegralsD, STIXIntegralsSm, STIXIntegralsUp, STIXIntegralsUpD, STIXIntegralsUpSm, STIXNonUnicode, STIXSizeFiveSym, STIXSizeFourSym, STIXSizeThreeSym, STIXSizeTwoSym, STIXVariants; font-style: italic; fill: black; background-color: transparent; 26.410α α , Glossary

a uniformly most powerful critical region of size α 2.1099999999999994α α ,

a uniformly most powerful test, , Glossary

an antithetic pair, The Continuous Case

an approximate poisson process, POISSON DISTRIBUTION, Glossary

an exponential distribution, An Exponential Distribution, Glossary

an unbiased estimator of simplemath mathml-miitalicsθ 1.18.94pt10.89pt0 0 8.94 10.892.1099999999999994none#000000optimizeLegibilitySTIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariantsfont-family: STIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariants; fill: ; background-color: transparent; font-family: STIXGeneral,STIXSizeOneSym,STIXIntegralsD,STIXIntegralsSm,STIXIntegralsUp,STIXIntegralsUpD,STIXIntegralsUpSm,STIXNonUnicode,STIXSizeFiveSym,STIXSizeFourSym,STIXSizeThreeSym,STIXSizeTwoSym,STIXVariants; fill: ; background-color: transparent; font-family: STIXGeneral, STIXSizeOneSym, STIXIntegralsD, STIXIntegralsSm, STIXIntegralsUp, STIXIntegralsUpD, STIXIntegralsUpSm, STIXNonUnicode, STIXSizeFiveSym, STIXSizeFourSym, STIXSizeThreeSym, STIXSizeTwoSym, STIXVariants; font-style: italic; fill: black; background-color: transparent; 28.78000000000000110θ θ , Glossary

an unbiased estimator of θ 2.1099999999999994θ θ , Properties of Estimators

area under p.d.f. curve to a equal to a value of c.d.f. curve at a point a,

bernoulli trials, BERNOULLI TRIALS AND THE BINOMIAL DISTRIBUTION

biased, Properties of Estimators, Glossary

binomial distribution,

cauchy distribution,

chi-square distribution, Chi-Square Distribution, Glossary

confidence interval, CONFIDENCE INTERVALS I, Glossary

congruential generators,

continuous type, RANDOM VARIABLES OF THE CONTINUOUS TYPE

cumulative distribution function, , Glossary

definition of exponential distribution, An Exponential Distribution, Glossary

definition of random variable, RANDOM VARIABLE OF DISCRETE TYPE, Glossary

definition of uniform distribution, The Uniform Distribution, Glossary

distributive operator, , Proof

expected value,

failure, BERNOULLI TRIALS AND THE BINOMIAL DISTRIBUTION, Bernoulli distribution

for example, , ,

for example,,

for illustration, ,

gamma function, Gamma Distribution, Glossary

gamma type, Gamma Distribution, Glossary

highly skewed,

how large should the sample size be to estimate a mean?, Size Sample

in general, Size Sample

is called an estimator of θ2.1099999999999994θ θ, Properties of Estimators

it means be equal to θ2.1099999999999994θ θ , Properties of Estimators

k = 10 heads,

k = 19 heads, Hypotheses Testing - Examples.

least squares estimation (lse), ESTIMATION

linear,

mathematical expectation, , Glossary

mathematical expectiation, MATHEMATICAL EXPECTIATION, Glossary

maximum likelihood estimation (mle), ESTIMATION, Maximum Likelihood Estimation

mean, , , , Chi-Square Distribution,

mean value ,

modulus m,

moments of the distribution ,

normal and gamma distributions, The Continuous Case

observations:, BINOMIAL DISTRIBUTION, POISSON DISTRIBUTION

p-value,

p.d.f.,

parameter space, Properties of Estimators

period,

poisson distribution, , Glossary

poisson proccess, POISSON DISTRIBUTION, Glossary

probability density function, RANDOM VARIABLES OF THE CONTINUOUS TYPE, , Glossary

proof, , The Continuous Case, The Discrete Case

p[ k<18 2.2300000000000004k<18 k<18 or k>32 2.2300000000000004k>32 k>32 ] <0.05 2.2300000000000004<0.05 <0.05 ., Hypotheses Testing - Examples.

p[ k≤10 3.0299999999999994k≤10 k≤10 or k≥40 3.0299999999999994k≥40 k≥40 ] ≈0.000025. 2.1400000000000006≈0.000025. ≈0.000025. ,

rectangular,

reject, , Hypotheses Testing - Examples.

sample space s, RANDOM VARIABLE OF DISCRETE TYPE

shift-register, A Shift-Register Generator

standard deviation,

student's distribution, THE t DISTRIBUTION

success, BERNOULLI TRIALS AND THE BINOMIAL DISTRIBUTION, Bernoulli distribution

summarizing,

super-duper, Combinations of Generators (Shuffling)

t distribution, THE t DISTRIBUTION, Glossary, Confidence Intervals for Means

t-distribution, THE t DISTRIBUTION

tail-end probability,

tausworthe generators, A Shift-Register Generator

the alternative hypothesis,

the binary random variable, The Discrete Case

the confidence coefficient, CONFIDENCE INTERVALS I, Glossary

the confidence interval for the variance σ2 2.1099999999999994σ2 σ 2 , Confidence Interval for Variances

the cycle length,

the distribution function, , Glossary

the efficiency,

the expected value, , MATHEMATICAL EXPECTIATION, Glossary

the exponential distribution, The Continuous Case

the following is the general expression of the binomial pdf for arbitrary values of θ 2.1099999999999994θ θ and n:, Likelihood function

the gamma distribution, Gamma Distribution, Glossary

the generalized factorial, Gamma Distribution

the geometric distribution, The Discrete Case

the goal of data analysis is to identify the population that is most likely to have generated the sample., Likelihood function

the graph of the p.d.f. of the exponential distriution, THE UNIFORM AND EXPONENTIAL DISTRIBUTIONS

the graph of the p.d.f. of the uniform distriution,

the identity function, RANDOM VARIABLE OF DISCRETE TYPE, Glossary

the inverse of the gamma distribution function, which is given by, The Continuous Case

the lagged fibonacci generators, Fibonacci Generators

the likelihood function,

the mathematical expectation, , MATHEMATICAL EXPECTIATION, Glossary

the maximum error of the estimate,

the maximum error of the point estimate, Size Sample

the maximum likelihood estimator,

the maximum period,

the mean,

the mean of the distribution,

the mean of the empirical distribution,

the method of maximum likelihood, Method of Moments

the method of moments, Method of Moments

the mle estimate, Maximum Likelihood Estimation

the neyman-pearson lemma,

the normal and gamma distributions, The Continuous Case

the null hypothesis,

the parameter λ 2.16λ λ is the mean of the poisson distribution,

the parameters of the binomial distribution,

the probability density function,

the probability density function (p.d.f.), RANDOM VARIABLES OF THE CONTINUOUS TYPE, Glossary

the probability value,

the random variable of interest is the number of trials needed to observe the rth success, GEOMETRIC DISTRIBUTION

the rao-cramer inequality,

the rth factorial moment,

the rth moment of the distribution,

the rth moment of the distribution about b,

the seed,

the significance level of the test,

the standard deviation of x,

the standard error of the mean, TESTS ABOUT ONE MEAN AND ONE VARIANCE

the support of x,

the unbiased minimum variance estimator, ,

the unbiased minimum variance estimator of θ 2.1099999999999994θ θ , Properties of Estimators

the variance,

the variance of the empirical distribution,

the waiting times, An Exponential Distribution

theorem, The Discrete Case

theorem i, , The Continuous Case

theorem ii,

theorem iii,

theorem iv,

theorem v,

to illustrate the idea of a pdf, Likelihood function

type i error,

type i error:,

type ii error,

type ii error:,

unbiased and biased estimators, Properties of Estimators

variance, , , , <