Probability and Statistics with Applications

Department: 
MATH
Course Number: 
3670
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every Semester

Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.

Prerequisites: 

MATH 2401 or MATH 24X1 or MATH 2411 or MATH 2551 or MATH 2550 or MATH 2X51

Course Text: 

At the level of Probability & Statistics for Engineering and the Sciences, 8th edition, Devore, Thomson Learning

Topic Outline: 
  • Probabilities of Events:
    Random experiments, events, sets, and probabilities
    Probabilities for equally likely outcomes, elementary counting
    Independent events
    Conditional probability, Bayes theorem
    Applications
  • Random Variables and Their Distributions:
    Discrete random variables: Binomial, geometric, Poisson, multinomial
    Continuous random variables: Exponential, normal, gamma, Weibull
    Poisson process, waiting times
    Applications
  • Expected Values and Functions of Random Variables:
    Expectations and variances of standard random variables
    Expectations of functions of random variables
    Chi-square as the square of a normal, sums of independent random variables and reproductive properties of standard distributions
    Central limit theorem
    Applications
  • Descriptive Statistics:
    Random samples: data collection and presentation
    Sample statistics: mean, median, quantiles
  • Statistical Estimation:
    Point estimates and their properties
    Probability distributions for estimator, the t and F distributions
    Confidence intervals
  • Hypothesis Testing:
    Single sample tests, means, variances
    Comparison of two populations, means and variances
    Applications
  • Simple Linear Regression and Correlation:
    Fitting a regression line
    Inferences on the regression
    Predictions for future responses
    Correlation
    Applications