1 / 14

Discrete Distributions

Discrete Distributions. Random Variable -. A numerical variable whose value depends on the outcome of a chance experiment. Two types:. Discrete – count of some random variable Continuous – measure of some random variable. Discrete Probability Distribution.

virginiamanning
Download Presentation

Discrete Distributions

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discrete Distributions

  2. Random Variable - • A numerical variable whose value depends on the outcome of a chance experiment

  3. Two types: • Discrete – count of some random variable • Continuous – measure of some random variable

  4. Discrete Probability Distribution • Gives the values associated with each possible x value • Usually displayed in a table, but can be displayed with a histogram or formula

  5. Properties for a discrete probability distribution • For every possible x value, 0 < P(x) < 1. 2) For all values of x, Σ P(x) = 1.

  6. Suppose you toss 3 coins & record the number of heads. The random variable X defined as ... Create a probability distribution. Create a probability histogram. The number of heads tossed X 0 1 2 3 P(X) .125 .375 .375 .125

  7. Let x be the number of courses for which a randomly selected student at a certain university is registered. X 1 2 3 4 5 6 7 P(X) .02 .03 .09 ? .40 .16 .05 P(x = 4) = P(x < 4) = P(x < 4) = What is the probability that the student is registered for at least five courses? Why does this not start at zero? .25 .14 P(x > 5) = .61 .39

  8. Formulas for mean & variance Found on formula card!

  9. Let x be the number of courses for which a randomly selected student at a certain university is registered. X 1 2 3 4 5 6 7 P(X) .02 .03 .09 .25 .40 .16 .05 What is the mean and standard deviations of this distribution? μ = 4.66 & σ = 1.2018

  10. X 0 5 20 P(X) 7/9 1/6 1/18 Here’s a game: If a player rolls two dice and gets a sum of 2 or 12, he wins $20. If he gets a 7, he wins $5. The cost to roll the dice one time is $3. Is this game fair? A fair game is one where the cost to play EQUALS the expected value! NO, since m = $1.944 which is less than it cost to play ($3).

  11. If x is a random variable and a and b are numerical constants, then the random variable y is defined by and Linear function of a random variable The mean is changed by addition & multiplication! The standard deviation is ONLY changed by multiplication!

  12. Let x be the number of gallons required to fill a propane tank. Suppose that the mean and standard deviation are 318 gal. and 42 gal., respectively. The company is considering the pricing model of a service charge of $50 plus $1.80 per gallon. Let y be the random variable of the amount billed. What is the mean and standard deviation for the amount billed? μ = $622.40 & σ = $75.60

  13. Linear combinations Just add or subtract the means! If independent, always add the variances!

  14. A nationwide standardized exam consists of a multiple choice section and a free response section. For each section, the mean and standard deviation are reported to be mean SD MC 38 6 FR 30 7 If the test score is computed by adding the multiple choice and free response, then what is the mean and standard deviation of the test? μ = 68 & σ = 9.2195

More Related