Effective: 2018-01-01

Course Description

The course outline below was developed as part of a statewide standardization process.

General Course Purpose

The first part of the content provides understanding of the basic concepts of probability required for further study in statistics. The statistics content provides a solid foundation and training in some of the fundamental tools used by statistical practitioners.

Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 264 with a grade of C or better or equivalent.

Course Objectives

• Basic Concepts of Probability
• Relate the probability of an event to the likelihood of this event occurring.
• Explain how relative frequency is used to estimate the probability of an event.
• Determine the sample space of a given random experiment, including by using methods of enumeration.
• Demonstrate probabilities through simulations.
• Find the probability of events in the case in which all outcomes are equally likely.
• State and apply the laws of probability concerning these events.
• Use tools such as Venn Diagrams or probability tables as aids for finding probabilities.
• Explain the reasoning behind conditional probability, and how this reasoning is expressed by the definition of conditional probability.
• Find conditional probabilities and interpret them.
• Determine whether two events are independent or not.
• Use the general multiplication rule to find the probability that two events occur (p(a and b)).
• Use probability trees as a tool for finding probabilities.
• Understand the total probability and Bayes' theorem.
• Discrete Distributions
• Identify discrete random variable.
• Find the probability distribution of discrete random variables, and use it to find the probability of events of interest.
• Compute the expected value and variance of a discrete random variable, and apply these concepts to solve real-world problems.
• Explain the concepts of Bernoulli Trials and discrete models such as binomial distribution, geometric, negative binomial distribution, hypergeometric distribution, and Poisson Distribution.
• Recognize the situations to which each of the distributions is applicable, and solve applied problems.
• Find the mean and variance using the moment generating function.
• Continuous Distributions
• Distinguish between discrete and continuous random variables
• Explain how a density function is used to find probabilities involving continuous random variables.
• Compute the expected value and variance of each of the distributions studied.
• Find probabilities associated with the normal distribution.
• Perform probabilities associated with uniform, exponential distributions, gamma, chi-square distributions, Weibull Distribution, joint probability distributions, and mixed type distributions.
• Recognize the situations to which each of the distributions is applicable, and solve applied problems.
• Bivariate Distributions
• Compute probabilities, marginal densities, conditional densities and conditional probabilities for multivariate probability distributions.
• Compute the expected value, variance and covariance of each of the multivariate distributions studied.
• Apply the rules of means and variances to find the mean and variance of a linear transformation of a random variable and the sum of two independent random variables.
• Graphically display the relationship between two quantitative variables and describe: a) the overall pattern, and b) striking deviations from the pattern.
• Interpret the value of the correlation coefficient, and be aware of its limitations as a numerical measure of the association between two quantitative variables.
• Perform bivariate normal distribution problems
• Distributions of Functions of Random Variables
• Use transformation of a random variable to find probability distributions for functions of one random variable.
• Use moment generating functions to find the probability distributions for sums of random variables.
• Use transformations of two random variables to find the probability distribution.
• Compute with several independent random variables.
• Derive random functions associated with normal distribution
• Estimation
• Use basic statistical techniques in the analysis and interpretation of data in the various disciplines and physical phenomena.
• Determine point estimates in simple cases, and make the connection between the sampling distribution of a statistic, and its properties as a point estimator.
• Define and calculate maximum likelihood estimators of various distributions.
• Explain the application of the Central Limit Theorem to sampling distributions.
• Explain what a confidence interval represents and determine how changes in sample size and confidence level affect the precision of the confidence interval.
• Find confidence intervals for the mean, the difference between two means, a proportion, Perform simple regression analysis.
• Tests of Statistical Hypotheses
• Explain the logic behind and the process of hypotheses testing. Explain what the p-value is and how it is used to draw conclusions.
• Specify (in a given context) the null and alternative hypotheses for the appropriate population parameters.
• Carry out hypothesis testing for the population parameters, and draw conclusions in context.
• Apply the concepts of sample size, statistical significance vs. practical importance, and the relationship between hypothesis testing and confidence intervals.
• Determine the likelihood of making type i and type ii errors, and explain how to reduce them, in context.
• Determine confidence intervals for the least squares estimators.
• Estimate the regression coefficients.
• Find confidence intervals for the parameters of a regression model.
• Identify and distinguish among cases where use of calculations specific to independent samples, matched pairs, and ANOVA appropriate.
• Perform ANOVAs.(one-way)
• Nonparametric Methods
• Perform Chi-Square goodness of fit tests and Chi-square test for independence. (Chop 10)
• Technology Applications
• Demonstrate the application of statistics through a comprehensive project. [Instructors see pedagogical notes for details.]
• Use a statistical package to investigate and analyze data and to generate statistical information. [Instructors see pedagogical notes for details.]

Major Topics to be Included

• Basic Concepts of Probability
• Discrete Distributions
• Continuous Distributions
• Bivariate Distributions
• Distributions of Functions of Random Variables
• Estimation
• Tests of Statistical Hypotheses
• Nonparametric Methods
• Technology Applications