random variables n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Random Variables PowerPoint Presentation
Download Presentation
Random Variables

Loading in 2 Seconds...

play fullscreen
1 / 10
benedict-tyler

Random Variables - PowerPoint PPT Presentation

121 Views
Download Presentation
Random Variables
An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Discrete Random Variables: a random variable that can assume only a countable number of values. The value of a discrete random variable comes from counting. Continuous Random Variable: random variables that can assume any value on a continuum. Measurement is required to determine the value for a continuous random variable. Random Variables

  2. Continuous Probability Distributions The probability distribution of a continuous random variable is represented by a probability density function that defines a curve. The area under the curve corresponds to the probabilities for the random variable.

  3. Continuous Probability Distributions • The Continuous Uniform Distribution • A probability distribution in which the probability of a value occurring between two points, a and b, is the same as the probability between any other two points, c and d, given that the distance between a and b is equal to the distance between c and d. f (x) = 1 / ( b - a ) if a< x <b

  4. The Uniform Probability Density Function • Mean and standard deviation of the uniform probability density function:

  5. EXAMPLE Suppose the research department of a steel manufacturer believes that one of the company’s rolling machines is producing sheets of steel of varying thickness. The thickness is a uniform random variable with values between 150 and 200 millimeters. Any sheet less than 160 millimeters must be scrapped because they are unacceptable to buyers.

  6. EXAMPLE • Calculate the mean and standard deviation of x, the thickness of the sheets produced by this machine. Then graph the probability distribution and show the mean on the horizontal axis. • Calculate the fraction of steel sheets produced by this machine that have to be scrapped.

  7. Continuous Probability Distributions • The Normal Distribution • A bell-shaped, continuous distribution with the following properties: • It is unimodal; the normal distribution peaks at a single value. • It is symmetrical; 50% of the area under the curve lies left of the center and 50% lies right of the center. • The mean, mode, and median are equal. • It is asymptotic; the normal distribution approaches the horizontal axis on each side of the mean toward +

  8. The Normal Distribution The Normal Distribution is defined by two parameters:

  9. The Standard Normal Distribution The Standard Normal Distribution is a continuous, symmetrical, bell-shaped distribution that has a mean of 0 and a standard deviation of 1.

  10. The Z Score The Z Score is the number of standard deviations between the mean and the point X.