This module describes the aims and motivation for the course.
The purpose of this investigation is to have students analyze cloud cover and to compose written conclusions to a given related scenario.
This resource consists of a Java applet and expository text. The applet is a simulation of the ballot experiment: The votes in an election are randomly counted. The event of interest is that the winning candidate is always ahead in the vote count.
Finding the true probability of an event taking into account misses, false positives, and base rates. Also, using Bayes' Theorem.
This module contains a review of the basic concepts of probability.
Students play a game in which they place beans on numbers that represent the sum of two dice. Each time a number comes up in a dice roll, a corresponding bean may be removed. The first person who removes all his beans wins the game. Students mathematically analyze the game to develop strategies.
This resource consists of a Java applet and expository text. The applet is a simulation of Bertrand's experiment: a random chord on a circle The event of interest is whether the length of the chord is larger than the length of the inscribed equilateral triangle. Three models for generating the random chord can be used.
This resource consists of a Java applet and expository text. The applet illustrates Bayesian estimation of the probability of heads for a coin. The prior beta distribution, true probability of heads, and the sample size can be specified. The applet shows the posterior beta distribution.
This resource consists of a Java applet and expository text. The applet simulates a random sample from a beta distribution, and computes standard point estimates of the left and right parameters. The bias and mean square error are also computed.
This resource consist of a Java applet and expository text. The applet simulates Bernoulli trials in terms of coin tosses. The random variables of interest are the number of heads and the proportion of heads. The number of coins and the probability of heads can be varied. The applet illustrates the law of large numbers and the central limit theorem.
This resource consists of a Java applet and expository text. The applet simulates Bernoulli trials in terms of random points on a timeline. The random variables of interest are the number of successes and the proportion of successes. The number of trials and the probability of success can be varied. This applet illustrates the law of large numbers, the central limit theorem, and the binomial distribution.
This resource consists of a Java applet and expository text. The applet is a simulation of the birthday experiment: a sample of size n is chose at random and with replacement from the first m positive integers. The random variable of interest is the number of distinct sample values. The event of interest is that all sample values are distinct.
This resource consists of a Java applet and expository text. The applet simulates the bivariate normal distribution. The means are set at 0, but the standard deviations and the correlation can be varied. Simulated points from the distribution are shown as dots in a scatterplot.
This resource consists of a Java applet and expository text. The Java applet illustrates the bivariate uniform distribution on three types of regions: a square, a circle, and a triangle. Simulated points from the distribution are shown as dots in a scatterplot.
This resource consists of a Java applet and expository text. The applet simulates Buffon's coin experiment. The radius of the coin can be varied. The applet illustrates a random experiment, the sample space, random variables, events, probability, and relative frequency.
This resource consists of a Java applet and expository text. The applet simulates Buffon's needle experiment and the corresponding approximation of pi. The event of interest is that the needle crosses a crack. The length of the needle can be varied. The applet illustrates a random experiment, the sample space, random variables, probability, and relative frequency.
Submitted as part of the California Learning Resource Network (CLRN) Phase 3 Digital Textbook Initiative (CA DTI3), CK-12 Advanced Probability and Statistics introduces students to basic topics in statistics and probability but finishes with the rigorous topics an advanced placement course requires. Includes visualizations of data, introduction to probability, discrete probability distribution, normal distribution, planning and conducting a study, sampling distributions, hypothesis testing, regression and correlation, Chi-Square, analysis of variance, and non-parametric statistics.
This resource consists of a Java applet and expository text. The applet is a simulation of drawing n cards from a standard deck. The parameter n can be varied.
This activity will allow students to familiarize themselves with technology and its use in calculating marginal, conditional, and joint distributions, as well as making conclusions from these tabular and graphical displays.
The applets in this section of Statistical Java allow you to see how the Central Limit Theorem works. The main page gives the characteristics of five non-normal distributions (Bernoulli, Poisson, Exponential, U-shaped, and Uniform).
