1. Statistics 3502/6304 Prof. Eric A. Suess Chapter 4

2. Introduction to Probability Random Variables – Discrete and Continuous Probability Distributions for Discrete Random Variables Binomial Distribution Probability Distribution for Continuous Random Variables Normal Distribution

3. Random Variables – Discrete and Continuous Qualitative Random Variables – Categories No - Yes, 0 - 1 Quantitative Random Variables – Counts 0,1,2,…. X > 0 When observation on a quantitative random variable can assume only a countable number of values, the variable is called a discrete random variable. When observations on quantitative random variables can assume one of the uncountable number of values on a line interval, the variables is called a continuous random variable.

4. Probability Distributions for Discrete Random Variables

5. Binomial Distribution Many random experiments count the number of successes in a certain number of trials. When the following properties hold the experiment is call a Binomial Experiment 1.The experiment consists of n identical trials. 2.Each trial results in one of two outcomes. Success or Failure. 3.The probability of success on a single trial remains the same. 4.The trials are independent. 5.The random variable Y is the number of success observed during the n trials.

6. Binomial Distribution

7. Binomial probabilities can be computed using: The formula on the previous slide. Using Minitab Calc > Probability Distributions > Binomial… Using MS Excel See Example 4.8

8. Binomial Distribution

9. Probability Distribution for Continuous Random Variables