  Principles of data reduction, point estimation theory (MLE, Bayes, UMVU), hypothesis testing, interval estimation, decision theory, asymptotic evaluations.  Senior    Collective risk models, moment and mgf of aggregate claims, recursion formulae, effect of reinsurance, individual risk model, De Pril’s recursion formula and Komya’s method, premium principles: risk adjusted principle, applications of utility theory, reinsurance problems, ruin theory. Applications of contingency theory in life and health insurance. Loss distributions.  Junior    Distributions of random variables; conditional probability and stochastic independence; some special distributions (discrete and continuous distributions); univariate, bivariate and multivariate distributions; distributions of functions of random variables (distribution function method, moment generating function method, and the Jacobian transformation method); limiting distributions.  Sophomore & Junior    Mathematical & Statistical techniques in compound interest, discounted cash flow, valuation of cash flows of insurance contracts, analysis and valuation of annuities, bonds, loans and other securities. Yield curves and immunization. Stochastic interest rate models. Actuarial applications.  Junior    Mathematical & Statistical techniques in: the survival function, construction of life tables, Laws of mortality, Life insurance. Continuous and discrete distributions for life annuities. Recursion equations. Benefit premium modes and their relationship to annuity. Apportion able premiums. Continuous and discrete probability distribution for benefit reserves. Distribution models for insurance expenses.  Junior    Markov chains, transition probability, classification of states, branching and queueing chains, stationary distributions of Markov chain, Markov pure jump processes; second order processes, mean and covariance functions, Gaussian Process and Wiener process.  Third year    Quantitative analysis and interpretation of health data including probability distributions, estimation of effects, and hypothesistests such as chisquare, oneway ANOVA, and simple linear regression.  Master level    Principles of data reduction, point estimation theory (MLE, Bayes, UMVU), hypothesis testing, interval estimation, decision theory, asymptotic evaluations.  Master level    Describing statistical data by tables, graphs and numerical measures, Chebychev’s inequality and the empirical rule, counting methods, combinations, permutations, elements of probability and random variables, the binomial, the Poisson, and the normal distributions, sampling distributions, elements of testing hypotheses, statistical inference about one and two populations parameters.  Freshman    Comparisons Involving Means, Experimental Design, and Analysis of Variance. Comparison Involving Proportions. Simple Linear Regression. Multiple Linear Regression. Nonparametric Tests.     Functions ( exponential and logarithmic ) and limits , continuity of trigonometric , exponential and inverse function ,derivative of function , Application of derivative ( increasing , decreasing and concavity ) , integral and application of derivative.     Techniques of integration: integration by parts, integration by substitution, integration by partial fraction.
Applications of the definite integral to find length of plane curves, area between two plane curves, area of surfaces of revolution volume of solids of revolution.
Sequences and series: convergence of sequence and series, Maclaurin and Taylor series.  
