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.

MATH 3215, MATH 3235, MATH 3670, and MATH 3740 are mutually exclusive; students may not hold credit for more than one of these courses. 

Prerequisites: 

MATH 2550 or MATH 2551 or MATH 2561 or MATH 2X51 

Course Text: 

Introduction to Probability and Statistics for Engineers and Scientists, 5th edition, by Sheldon M. Ross

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