丁香园AV

Designed for students specializing in mathematics, physics, chemistry, computing science and engineering. Logarithmic and exponential functions, trigonometric functions, inverse functions. Limits, continuity, and derivatives. Techniques of differentiation, including logarithmic and implicit differentiation. The Mean Value Theorem. Applications of Differentiation including extrema, curve sketching, related rates, Newton's method. Antiderivatives and applications. Conic sections, polar coordinates, parametric curves. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least A, or MATH 100 with a grade of at least B, or achieving a satisfactory grade on the 丁香园AV Calculus Readiness Test. Students with credit for either MATH 150, 154 or 157 may not take MATH 151 for further credit. Quantitative.

Riemann sum, Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, applications of integration. First-order separable differential equations. Sequences and series, series tests, power series, convergence and applications of power series. Prerequisite: MATH 150 or 151; or MATH 154 or 157 with a grade of at least B. Students with credit for MATH 155 or 158 may not take this course for further credit. Quantitative.

Chance phenomena and data analysis are studied through simulation and examination of real world contexts including sports, investment, lotteries and environmental issues. Intended to be particularly accessible to students who are not specializing in Statistics. Students with credit for STAT 101, 201, 203, 270 or BUEC 232 will not receive additional credit for this course. Quantitative/Breadth-Science.

The collection, description, analysis and summary of data, including the concepts of frequency distribution, parameter estimation and hypothesis testing. To receive credit for both STAT 100 and STAT 101, STAT 100 must be taken first. Intended to be particularly accessible to students who are not specializing in Statistics. Students with credit for STAT 102, 201, 203 (formerly STAT 103), 301, MATH 101 or 102 may not take STAT 101 for further credit. Students with credit for ARCH 376, BUEC 232 (formerly 332) or STAT 270 (formerly MATH 272 and 371) may not subsequently receive credit for STAT 101-3. Quantitative.

Research methodology and associated statistical analysis techniques for students with training in the life sciences. Intended to be particularly accessible to students who are not specializing in Statistics. Prerequisite: 30 units. Students with credit for STAT 101, 102, 203 (formerly 103), 270 (formerly MATH 272) or 301 may not take STAT 201 for further credit. Quantitative.

Descriptive and inferential statistics aimed at students in the social sciences. Scales of measurement. Descriptive statistics. Measures of association. Hypothesis tests and confidence intervals. Students in Sociology and Anthropology are expected to take SA 255 before this course. Intended to be particularly accessible to students who are not specializing in Statistics. Prerequisite: Recommended: SA 255, CRIM 120, POL 213 or equiv. Students with credit for STAT 101, 102, 103, 201, 270, ARCH 376 or, BUEC 232 (formerly 332), may not subsequently receive credit for this course. Quantitative.

The standard techniques of multiple regression analysis, analysis of variance, and analysis of covariance, and their role in experimental research. Prerequisite: Any STAT course (except STAT 100), or BUEC 232, or ARCH 376. Statistics major and honors students may not use this course to satisfy the required number of elective units of upper division statistics. However, they may include the course to satisfy the total number of required units of upper division credit. Students cannot obtain credit for STAT 302 if they already have credit for STAT 305 and/or 350. Quantitative.

A practical introduction to useful sampling techniques and intermediate level experimental designs. Statistics minor, major and honors students may not use this course to satisfy the required number of elective units of upper division Statistics. However, they may include the course to satisfy the total number of required units of upper division credit. Intended to be particularly accessible to students who are not specializing in Statistics. Prerequisite: STAT 302, 305 or 350. Students with credit for STAT 410 or 430 may not take STAT 403 for further credit. Quantitative.

Basic laws of probability, sample distributions. Introduction to statistical inference and applications. Corequisite: MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Quantitative. Prerequisite: COREQ-MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Equivalent Courses: STAT102 STAT103 STAT201 STAT203 STAT301. Quantitative.

This course is a continuation of STAT 270. Review of probability models, procedures for statistical inference from survey results and experimental data. Statistical model building. Elementary design of experiments and regression methods. Introduction to categorical data analysis. Prerequisite: STAT 270. Prerequisite or corequisite MATH 232 or MATH 240. This course may not be taken for credit by students who have credit for STAT 330 prior to Fall 2003. Quantitative.

Guided experiences in written and oral communication of statistical ideas and results with both scientific and lay audiences. Prerequisite: 丁香园AV to the major or honors programs in statistics or actuarial science at 丁香园AV. Corequisite: STAT 350. Students with credit for STAT 300 may not take this course for further credit. Writing.

Review of probability and distributions. Multivariate distributions. Distributions of functions of random variables. Limiting distributions. Inference. Sufficient statistics for the exponential family. Maximum likelihood. Bayes estimation, Fisher information, limited distributions of MLEs. Likelihood ratio tests. Prerequisite: STAT 285 and MATH 251. Quantitative.

Theory and application of linear regression. Normal distribution theory. Hypothesis tests and confidence intervals. Model selection. Model diagnostics. Introduction to weighted least squares and generalized linear models. Prerequisite: STAT 285 and MATH 251. Quantitative.

Review of discrete and continuous probability models and relationships between them. Exploration of conditioning and conditional expectation. Markov chains. Random walks. Continuous time processes. Poisson process. Markov processes. Gaussian processes. Prerequisite: STAT 330. Quantitative.

An introduction to the major sample survey designs and their mathematical justification. Associated statistical analyses. Prerequisite: STAT 350. Quantitative.

An extension of the designs discussed in STAT 350 to include more than one blocking variable, incomplete block designs, fractional factorial designs, and response surface methods. Prerequisite: STAT 350 (or MATH 372). Equivalent Courses: MATH404. Quantitative.

Distribution theory, methods for constructing tests, estimators, and confidence intervals with special attention to likelihood methods. Properties of the procedures including large sample theory. Prerequisite: STAT 330. Quantitative.

The Bayesian approach to statistics is an alternative and increasingly popular way of quantifying uncertainty in the presence of data. This course considers comparative statistical inference, prior distributions, Bayesian computation, and applications. Prerequisite: STAT 330 and 350. Quantitative.

Measurement of interest, present value. Equations of value. Basic annuities: immediate, due, perpetuity. General annuities. Yield rates: cash flow analysis, reinvestment rate, portfolio and investment year methods. Amortization schedules and sinking funds. Bonds and other securities. Applications: real estate mortgages depreciation methods. Interest rate disclosure and regulation in Canada. Covers the interest theory portion of Exam FM of the Society of Actuaries. Prerequisite: MATH 152. Students with credit for ACMA 310 may not take this course for further credit. Quantitative.

Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations. Prerequisite: MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 240 make not take this course for further credit. Quantitative.

Basic laws of probability, sample distributions. Introduction to statistical inference and applications. Corequisite: MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Quantitative. Prerequisite: COREQ-MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Equivalent Courses: STAT102 STAT103 STAT201 STAT203 STAT301. Quantitative.

This course is a continuation of STAT 270. Review of probability models, procedures for statistical inference from survey results and experimental data. Statistical model building. Elementary design of experiments and regression methods. Introduction to categorical data analysis. Prerequisite: STAT 270. Prerequisite or corequisite MATH 232 or MATH 240. This course may not be taken for credit by students who have credit for STAT 330 prior to Fall 2003. Quantitative.

Survival distributions: age at death, life tables, fractional ages, mortality laws, select and ultimate life tables. Life insurance: actuarial present value function (apv), moments of apv, basic life insurance contracts, portfolio. Life annuities: actuarial accumulation function, moments of apv, basic life annuities. Net annual premiums: actuarial equivalence principle, loss function, accumulation type benefits. Actuarial reserves: prospective loss function, basic contracts, recursive equations, fractional durations. Covers part of the syllabus for Exam M of the Society of Actuaries and Exam 3 of the Casualty Actuarial Society, and covers practical applications such as computational aspects of pricing and reserving, and risk measurement of insurance portfolios. Prerequisite: STAT 285 and ACMA 210 (with a grade of C+ or higher). Quantitative.

Limited fluctuation credibility theory: full credibility, partial credibility. Greatest accuracy credibility theory: the Bayesian methodology, the credibility premium, the Buhlmann model, the Buhlmann-Straub model, exact credibility, linear versus Bayesian versus no credibility. Empirical Bayes parameter estimation: nonparametric estimation, semiparametric estimation, parametric estimation. Simulation: basics of simulation, simulation in actuarial modeling. Covers part of the syllabus for Exam C of the Society of Actuaries, and Exam 4 of the Casualty Actuarial Society. Prerequisite: STAT 285. Quantitative.

Basic distributional quantities: moments, percentiles, generating functions and sums of random variables. Classifying and creating distributions. Frequency and severity with coverage modifications: deductibles, the loss elimination ratio and the effect of inflation for ordinary deductibles, policy limits, coinsurance. Aggregate loss models. Multi-state transition models with actuarial applications: non-homogeneous Markov chains, cash flows and their actuarial present values. The exponential distribution and the Poisson process. Covers part of the syllabus for Exam M of the Society of Actuaries, and Exam 3 of Casualty Actuarial Society. Prerequisite: ACMA 320. Quantitative.

Topics in areas of actuarial science not covered in the regular certificate curriculum of the department. Prerequisite: Dependent on the topics covered.

Actuarial reserves: allocation of the loss to the policy years. Multiple life functions: joint-life, last-survivor. Multiple decrement models: stochastic and deterministic approaches, associated single decrement, fractional durations. Valuation theory for pension plans. Insurance models including expenses: gross premiums and reserves, type of expenses, modified reserves. Nonforfeiture benefits and dividends: equity concept, cash values insurance options, asset shares, dividends. Covers part of the syllabus for Exam M of the Society of Actuaries and Exam 3 of the Casualty Actuarial Society. Prerequisite: ACMA 320. Quantitative.

Quality of an estimator: unbiasedness, asymptotic unbiasedness, consistency, means squared error, uniform minimum variance. Confidence interval. Tests of hypotheses. Estimation for complete data. Estimation for grouped data. Estimation for modified data: Kaplan-Meier estimator, variances and confidence intervals of the empirical estimator, kernel density estimator. Parameter estimation. Variance of the estimators and confidence intervals. Model selection: graphical procedures, goodness-of-fit test, likelihood ratio test. Interpolation and smoothing. Covers part of the syllabus for Exam C of the Society of Actuaries and Exam 4 of the Casualty Actuarial Society. Prerequisite: ACMA 320. Quantitative.

The topics included in this course will vary from term to term depending on faculty availability and student interest. Prerequisite: Dependent on the topic covered.

Independent study and/or research in topics chosen in consultation with the supervising instructor. Prerequisite: written permission from the Department of Statistics and Actuarial Science undergraduate curriculum committee.

A presentation of the problems commonly arising in numerical analysis and scientific computing and the basic methods for their solutions. Prerequisite: MATH 152 or 155 or 158, and MATH 232 or 240, and computing experience. Quantitative.

Linear programming modelling. The simplex method and its variants. Duality theory. Post-optimality analysis. Applications and software. Additional topics may include: game theory, network simplex algorithm, and convex sets. Prerequisite: MATH 150, 151, 154, or 157 and MATH 240 or 232. Quantitative.

Review of probability and distributions. Multivariate distributions. Distributions of functions of random variables. Limiting distributions. Inference. Sufficient statistics for the exponential family. Maximum likelihood. Bayes estimation, Fisher information, limited distributions of MLEs. Likelihood ratio tests. Prerequisite: STAT 285 and MATH 251. Quantitative.

Theory and application of linear regression. Normal distribution theory. Hypothesis tests and confidence intervals. Model selection. Model diagnostics. Introduction to weighted least squares and generalized linear models. Prerequisite: STAT 285 and MATH 251. Quantitative.