Geogebra Worksheets Portfolio

Jose Alvarado, Jun 22, 2015

This Geogebrabook contains 5 worksheets that could help teachers explain some probability topics [list] [*]Mean, variation and standard distribution [*] Poisson distribution [*] Binomial distribution [*] Venn Diagrams [*] Bayes' Theorem [/list] Elaborated by : José J. Alvarado Rodríguez June 2015

Table of Contents

  1. Mean, Variation and Standard Distribution
    1. Mean, variation, standard distribution
  2. Distributions
    1. Poisson Distribution
    2. Binomial Distribution
  3. Venn Diagram
    1. Venn Diagram
  4. Bayes' Theorem
    1. Bayes' Theorem

1.

Mean, Variation and Standard Distribution

This chapter explain what the mean, variation and standard distribution is with an example for the user to complete

  • 1. Mean, variation, standard distribution

1.1.

Mean, variation, standard distribution

Definitions
These three concepts are the basics of the following topics, therefore it is very important to understand them.[br][br][list][list] [b][*] Mean[/b]: The mean usually refers either to the expected value of a random variable or to the arithmetic average of a set of data [b][*]Variance:[/b] A measure of variability defined as the expected value of the square of the random variable around its mean[b][*] Standard Deviation:[/b] The positive square root of the variance. The standard deviation is the most widely used measure of variability.[/list][/list]
– Jose Alvarado

2.

Distributions

This Chapter contains [list] [*] Poisson Distribution [*] Binomial Distribution . [/list] [list=1] [*]The Poisson distribution is a discrete probability distribution that express the probability of a given number of events occurring in a fixed interval of time or space. A discrete random variable X is said to have a Poisson distribution with parameter λ > 0, if, for k = 0, 1, 2, …, the probability mass function of X is given by: [url]https://upload.wikimedia.org/math/a/b/3/ab327bb7e6cf7f72071e92b9e3ba42ee.png[/url] . [*] The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. The probability of getting exactly k successes in n trials is given by the probability mass function: [url]https://upload.wikimedia.org/math/1/d/5/1d53e4a0d17e17adfeb7f53ecca9df5d.png[/url] [/list]

  • 1. Poisson Distribution
  • 2. Binomial Distribution

2.1.

Poisson Distribution

Poisson Distribution
Here is an example of a Poisson Distribution:[br][br][list][br][*] Let Lambda be the mean of people making line at a random moment.[br][*] Select the number of people making line at that random moment.[br][*] What is the probability of X persons making line at that moment?.[br][/list][br][br][b]Play with the sliders and find out the answer[/b]
– Jose Alvarado

2.2.

–

3.

Venn Diagram

This chapter explain the concept of Venn Diagrams and presents an example for the user to complete

  • 1. Venn Diagram

3.1.

Venn Diagram

Venn Diagram
[list][*]A Venn diagram or set diagram is a diagram that shows all possible logical relations between a finite collection of different sets.[/*][/list][br][b]Being said that:[/b][br][br]In this example you can verify some of the possible logical relation between 2 different sets. [br][list][*]You can select each relation by clicking each box.[/*][*]What other relations can you think of?.[br][/*][/list]
– Jose Alvarado

4.

Bayes' Theorem

This chapter explain the Bayes' Theorem and presents an example for the user to complete

  • 1. Bayes' Theorem

4.1.

Bayes' Theorem

Bayes' Theorem definition
The Bayes' Theorem is defined by the following statement:[br][br][list][*][b]An equation for a conditional probability such as[math] [math]P[/math][/math](A | B) in terms of the reverse conditional probability P (B | A).[/b][/*][/list]The following example is one of the most famous representations of this theorem.
– Jose Alvarado

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