Math 4030 Final Exam Review. Probability (Continuous) Definition of pdf (axioms, finding k) Cdf and probability (integration) Mean and variance (short-cut.

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Presentation transcript:

Math 4030 Final Exam Review

Probability (Continuous) Definition of pdf (axioms, finding k) Cdf and probability (integration) Mean and variance (short-cut formula) Properties of Mean and variance (linearity, independent, …) Continuous distribution: Uniform, Normal, Gamma (Exp, Chi-square as special cases), Beta, Weibull. (Mean, variance, tables, integral for simple values of parameters) Use of Tables: normal, t, chi-square, F. Two RV’s: joint, marginal, conditional, independency, mean and variance, covariance. (Double integration.) (Are X and Y independent?)

All about Normal: Properties of normal distribution: parameters, standard normal, mean and variances, linear combinations; Find probabilities; Find the cut-off scores, z  notation; Normal approximate binomial, correction for continuity.

Sample Statistics and Their Distributions: Sample means distribution (t or z?) Central Limit Theorem and application Sample variance and standard deviation (Chi-square or F?) Sample proportion: binomial and normal Sample size calculation.

Confidence intervals: Concepts: point estimation, maximum error, and confidence level; C.I. for population mean  ; C. I. for difference of two means; C.I. for population variance or standard deviation; C.I. for population proportion; C. I. for difference of two proportions; C.I. for parameters in linear regression; C.I. for correlation coefficient.

Hypothesis Testing: Concepts: Null vs. Alternative hypotheses, tails, critical value(s), critical region, P-value, types of errors, conclusion. Hypothesis testing regarding Mean from one sample (z or t); Mean from two samples (dependent or independent? Equal or unequal variances? Z or t?); Proportion from one sample; Proportion from several samples (r by c table); Goodness of Fit Test; Slope and intercept in the linear regression; Correlation coefficient.

General Procedure: 1.Null and alternative hypotheses (what is the claim?) (1 point) 2.Level of significance (left-tail, right-tail, or two-tail test) (1 point) 3.Decide the distribution to use and find the critical value(s) or region. Calculate the corresponding z-score, t-score, chi-square score, or F-score, from the sample statistics. (2 points) 4.Conclusion (1 point) Reject or not reject the null hypothesis Make comment about the claim.

Linear regression: Concepts: identify the linear correlation from scatter plots; Calculate correlation coefficient: strength vs. significance. Find Linear regression line: method of the least squares Prediction and errors; Meaning of correlation coefficient, slope of the regression line, and coefficient of determination (r-squared)

What to bring and what not to bring: Allowed: Non-programmable calculator; 2 page (4-side) letter size formula sheet. Not allowed: Textbook and any notes beyond 2 page limit; Calculator that are built in any other electronic device (tablets, cellphone, etc.) No need to bring: z-table, t-table, chi-square table, and F-tables.

Need extra help? Office Hours (RB 2007): Thursday Dec. 3: 9:00 – 11:00 AM Tuesday Dec. 8: 9:00 – 11:00 AM Friday Dec. 11: 9:00 – 11:00 AM LUMAC (Li 2004)