1 / 53

Random Variables

Random Variables. OBJECTIVE. Construct a probability distribution. Find measures of center and spread for a probability distribution. RELEVANCE. To find the likelihood of all possible outcomes of a probability distribution and to describe the distribution. Definition…….

tbible
Télécharger la présentation

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. 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. Random Variables

  2. OBJECTIVE • Construct a probability distribution. • Find measures of center and spread for a probability distribution.

  3. RELEVANCE To find the likelihood of all possible outcomes of a probability distribution and to describe the distribution.

  4. Definition…… • Random Variable – a random variable, x, represents a numerical value associated with each outcome of a probability experiment; values are determined by chance (Mutually exclusive)

  5. You have 4 True or False questions and you observe the number correct. Random Variable (x) # correct Possible Values of x 0, 1, 2, 3, 4 Example……

  6. Count the number of siblings in your family. Random Variable (x) # of siblings Possible Values 0, 1, 2, 3, ….. Example……

  7. Toss 5 coins and observe the number of heads. Random Variable (x) # of heads Possible Values 0, 1, 2, 3, 4, 5 Example……

  8. 2 Types of Random Variables…… • Discrete – can be counted Ex: # of joggers • Continuous – can be measured Ex: Height, Weight, Temp, Time, Distance

  9. Probability Distributions – Discrete ……

  10. Probability Distribution…… • Consists of the values a random variable can assume and the corresponding probabilities of the variables. • The probabilities used are theoretical.

  11. Construct a probability distribution of tossing 2 coins and getting heads. Remember: x = the number of heads possible p(x) = the probability of getting those heads Example……

  12. The sample space for tossing 2 coins consists of TT HT TH HH The probability distribution of getting heads… Answer……

  13. Now Graph It……

  14. Construct a probability distribution of tossing 3 coins and getting heads. Remember: x = the # of heads possible P(x) = the probability of getting those heads Example……

  15. The sample space of tossing 3 coins consists of HHH THH HHT THT HTH TTH HTT TTT The probability distribution…. Answer……

  16. Graph It……

  17. Construct a probability distribution for rolling a die. The probability distribution…. Example……

  18. 1. Probability has to fall between 0 and 1 for individual probabilities 2. All the P(x)’s must add up to 1. 2 Requirements for a Probability Distribution……

  19. Is it a probability distribution?Example 1…… YES

  20. Example 2…… YES

  21. Example 3….. NO

  22. Example 4….. NO Individual P(x) does not fall between 0 and 1

  23. Complete the Chart…… 1 – 0.72 = 0.28

  24. Probability Functions

  25. Probability Function…… • A rule that assigns probabilities to the values of the random #’s.

  26. Example…… • The following function, is a probability distribution for x = 1, 2, 3, 4. Write the probability distribution.

  27. Answer…… • You can set a formula in the lists using your calculator by putting x’s in L1 and setting L2 as L1/10……or you can just plug it in by hand.

  28. Would the function • Be a probability distribution for x= 2, 3, 4, 5?

  29. Answer…… • Here is the distribution…… • The sum of the P(x) values adds up to a number greater than 1….therefore it is NOT a probability distribution.

  30. Example…… • Write the probability distribution for the function if x = 0, 1, 2

  31. Mean, Standard Deviation, and Variance of a Probability Distribution Section 5.3

  32. Take Note: Probability distributions may be used to represent theoretical populations, therefore, we will use population parameters and our symbols used will be for population values.

  33. Example…… • A. Find the mean, variance, and standard deviation. • B. Find the probability that • C. Find the probability that

  34. Mean: • We are going to do this on our graphing calculator. • Put x’s in L1 and P(x) in L2. • Set a formula in L3: L1xL2 • The sum of this column is your mean.

  35. This is what it looks like on the calculator.

  36. Another way to sum a list….. • 2nd Stat • Math • Sum L(#) This is actually better because you can store the mean to a location

  37. You’ll need to add a L4 in your calculator. Set a formula to find the formula above. Variance:

  38. The sum of L4 is your variance.

  39. Standard Deviation: • The variance was 1.29.

  40. Remember that Remember that Find the x’s for which you should sum their probabilities: The x’s will be between 1.9 – 2(1.14) = -0.38 1.9 + 2(1.14) = 4.18 Find the probability that

  41. Remember: The x values are between -0.38 and 4.18. • All of our x’s fall in between these 2 values. • Add the probabilities that goes along with these values. • 0.2+0.1+0.3+0.4 = 1 • The answer is 1.

  42. Remember that Remember that Find the x’s for which you should sum their probabilities: The x’s will be between 1.9 – 1.14 = 0.76 1.9 + 1.14 = 3.04 Find the probability that

  43. Remember: The x values are between 0.76 and 3.04. • Only 3 of the x values fall between the values listed above. • Add the probabilities that go with those 3. • 0.1+0.3+0.4 = 0.8 • The answer is 0.8.

  44. Example…… • A. Set up the distribution for • B. Find the mean, variance, and standard deviation of the probability distribution. • C. Find the probability that

  45. Set up the distribution……

  46. Mean: • We are going to do this on our graphing calculator. • Put x’s in L1 and P(x) in L2. • Set a formula in L3: L1xL2 • The sum of this column is your mean.

  47. This is what it looks like on the calculator……

  48. You’ll need to add a L4 in your calculator. Set a formula to find the formula above. The sum of list 4 is the variance. Variance:

  49. Standard Deviation: • The variance was 0.555555555. • The standard deviation is 0.75.

More Related