MTH 2480 - Probability and Statistics

• Summarize data numerically and graphically
• Use software for statistical analysis
• Identify the difference between a population parameter and a sample statistic
• Apply the multiplication rule, permutations, and combinations to calculate the number of outcomes
• Apply rules of probability to calculate the probabilities of events
• Apply the law of total probability and Bayes’ theorem to calculate the probabilities of events
• Calculate expectation and variance of probability distributions
• Apply the binomial, Poisson, normal, and exponential distributions to calculate the probabilities of events
• Apply the Central Limit Theorem to calculate sampling probabilities
• Construct appropriate confidence intervals for population mean and proportion
• Perform hypothesis tests concerning the means and proportions of one or two populations
• Construct a linear regression model and perform an inference for the regression

• Differentiation of algebraic and transcendental functions
• Integration of algebraic and transcendental functions

• Measures of central tendency and dispersion
• Introduction to probability and the laws of probability
• Conditional probability and Bayes’ theorem
• Discrete probability distributions: Bernoulli, binomial, and Poisson
• Expectation and variance of a random variable
• The Central Limit Theorem
• Continuous probability distributions: normal, exponential
• One-sample confidence intervals and statistical inference
• One-sample hypothesis testing and statistical inference
• Two-sample confidence intervals and statistical inference
• Two-sample hypothesis testing and statistical inference
• Correlation and simple linear regression
• Analysis of variance (if time permits)