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)