1 / 10

Probability Distributions

Probability Distributions. Chapter 7. The random variable X has a single value for each outcome within an experiment Discrete variables have separate and equi -distant values from each other Ex. 1, 2, 3, and 4 Continuous variables have an infinite number of possible values Ex. 1.2367

elia
Télécharger la présentation

Probability 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. Probability Distributions Chapter 7

  2. The random variable X has a single value for each outcome within an experiment • Discrete variables have separate and equi-distant values from each other Ex. 1, 2, 3, and 4 • Continuous variables have an infinite number of possible values Ex. 1.2367 • The probability that X will take on a particular value is P(x) • If all the values are equally likely than you have a discrete uniform distribution • The formula is P(x) = 1/n • An expected value is the average of all possible outcomes of a probability experiment E(x) = x1 P(x1) + x2 P(x2) … + xnP(xn)

  3. Suppose you had eight 5cm straws, seven 3cm straws, and three 6cm straws • Show the probability distribution for the length of a given straw • Determine the expected length of a straw E(x) = x1P(x1) + x2 P(x2) …+xn P(xn) = (5)(8/18) + (3)(7/18) + (6)(3/18) = 2.2 + 1.2 + 1 = 4.4

  4. A binomial distribution has a specified number of independent trails in which the outcome is either success of failure • The probability of success is the same in each trail • The expectation for binomial distribution is E(x)= np • The probability is P(x) = (nCx)(p^x)(q^n-x)

  5. Example • 20% of the population is right handed • What is the probability that 4/10 people are right handed? • What is the expected number of right handed people? • P (success) =0.2 • Q (failure) =0.8 • P(x) = (10C4)(0.2^4)(0.8^6) • =0.09 • E(x) =np • =(10)(0.2) • =2

  6. A geometric distribution has a specified number of independent trails with two possible outcomes success or failure • It is either a success or failure once again, however you are counting the waiting time • The probability is P(x) = (q^x)(p) • The expectation of a geometric distribution is E(X) = q/p

  7. Example • You get a cake for an A- average • The probability of getting an A- on any one of the tests is 10% • What is the probability of getting the pizza on the 4th test? • P =0.1 • Q = 1 - 0.1 • = 0.9

  8. 7.4 Hypergeometric Distributions • A hypergeometric distribution has a specified number of dependant trails having the only possible outcomes success or failure • Probabilities are dependent and are not equal • The individual outcomes be repeated within these trails • P(x)= (aCx)(n-aCr-x) /nCr • The expectation for hypergoemetric distribution is E(x)= (r)(a)/n

  9. Example • Of 100 students, 50 are taking math, 5 are randomly selected • What is the probability that 3 are taking math?

  10. Activity • For each correct answer, you will be awarded a letter • Once you collect enough letters you have to unscramble them to make a word • The first group to make the word wins

More Related