MATH 2230 - Probability and Statistics

1. Algebraic skills, including facility with exponential and logarithmic functions
2. Facility with limits, derivatives, maximum/minimum problems
3. Basic techniques of integration for finding areas beneath curves

1. Calculate and analyze measures of central tendency and variability: mean, median, mode, range, variance, standard deviation, percentiles, and z-scores.
2. Construct and interpret visual summaries of data: frequency tables, histograms, box plots, and stem-and-leaf plots.
3. Understand basic concepts in probability, including combinatorics, independence, complementary events, conditional probability, and Bayes’ theorem.
4. Calculate probabilities using the addition and multiplication rules, the fundamental counting principle, permutations, combinations, and sample spaces.
5. Understand the concepts of random variables and probability distributions; construct a probability distribution for a random variable; distinguish between discrete and continuous probability distributions.
6. Understand the concept of mathematical expectation; calculate mean, variance and covariance of random variables.
7. Calculate and interpret expected values, variances, and probabilities for discrete probability distributions, such as binomial, geometric, negative binomial, hypergeometric, and Poisson, with an emphasis on binomial and Poisson.
8. Identify density functions and use methods from calculus to determine mean, variance, and probabilities of density functions.
9. Calculate and interpret expected values, variances, and probabilities for continuous probability distributions, such as uniform, gamma, exponential, chi-squared, with an emphasis on normal distributions.
10. Apply the Central Limit Theorem to describe the sampling distributions and calculate probabilities.
11. Construct and interpret confidence intervals of population means, proportions, and variances.
12. Create, perform, and interpret hypothesis tests of population means, proportions, and variances.
13. Perform chi-square tests of goodness of fit, independence, and homogeneity.
14. Interpret scatter plots as describing form, direction and strength of relationships in bi-variate data, and compute and interpret the correlation coefficient for linear bi-variate data.
15. Use linear regression to investigate correlation of paired data and to make predictions.
16. Perform analysis of variance.
17. Use statistical software to find descriptive statistics for a data set, display the data, find probabilities, perform basic statistical inference, and perform linear correlation and regression analysis.

1. Descriptive statistics
2. Probability and counting principles
3. Mathematical expectation
4. Discrete probability distributions
5. Density functions and continuous probability distributions
6. Sampling distributions and the Central Limit Theorem
7. Estimation and confidence intervals
8. Correlation and regression
9. Hypothesis testing
10. Analysis of variance