Mathematical Statistics 1
Time and Place
יום א 11:00 - 09:00 בקרייטמן-זלוטובסקי(חדש)  חדר 303
יום ג 18:00 - 16:00 בבנין 90 (מקיף ז’)  חדר 141
(1) Parametric point estimation: sampling, statistics, estimators, sample mean, sample variance, method of moments, maximum likelihood.(2) Properties of point estimators: mean square error, loss and risk functions, unbiased estimators, lower bound for variance (Rao-Cramer inequality), efficient estimators.(3) Sufficient statistics: factorization criterion, sufficiency and completeness, exponential families of distributions, finding of minimal variance unbiased estimators.(4) Parametric interval estimation: confidence interval, sampling from normal distribution, confidence intervals for mean and variance, large sample confidence interval.(5) Test of hypotheses: simple hypothese versus simple alternative, most powerful test, composite hypotheses, uniformly most powerful test, sampling from normal distribution, tests for mean and variance.(6) Comparison of two populations: confidence interval for differences of two means, test on two means, tests concerning variances, goodness of fit tests, tests on independence.