1. Chapter 12 Continuous Random Variables and their Probability Distributions

2. Probability Distributions of a Continuous Random Variable For a continuous random variable X, a probability density function such that

3. Probability Distributions of a Continuous Random Variable For a continuous random variable X, a probability cumulative function:

4. Mean & Standard Deviation of a Continuous Random Variable

5. Continuous Probability Distributions Continuous Uniform Distribution Normal Distribution Exponential Distribution Erlang and Gamma Distributions Weibull Distribution Lognormal Distribution Beta Distribution

6. Continuous Uniform Distribution Probability Density Function Mean Variance

7. Normal Distribution Probability Density Function, with parameter , where -  0 Mean Variance

8. Normal Distribution The curve is symmetric about the mean The mean, median, and mode are equal The tails of the curve extend indefinitely

9. Standard Normal Distribution A normal random variable with parameter  =0, and  =1 Cumulative Distribution: Table II in Appendix A Convert x to z

10. Standard Normal Distribution www.barringer1.com/jan98f1.gif -6  -5  -4  -3  -2  -1  01  2  3  4  5  6  

11. Exponential Distribution Probability Density Function, with mean, where >0, and x>0 Cumulative probability Mean Variance

12. Exponential Distribution

13. Exponential Distribution Alternate Definition Probability Density Function, with rate, where >0, and x  0 Cumulative probability Mean Variance

14. Exponential Distribution Example An HR department wishes to study the need for hiring new secretaries. It is estimated that the amount of time that a secretary stays in the job can be described as an exponential distribution with a mean of 26 months. The company just hired a new secretary. Calculate the probabilities of the following events: The secretary has to be replaced within the first year. The secretary has to be replaced during the third year. The secretary remains in the position for more than 5 years