1 / 19

Binomial Distribution

Binomial Distribution. What the binomial distribution is How to recognise situations where the binomial distribution applies How to find probabilities for a given binomial distribution, by calculation and from tables. When to use the binomial distribution. Independent variables.

jspencer
Download Presentation

Binomial Distribution

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. Binomial Distribution What the binomial distribution is How to recognise situations where the binomial distribution applies How to find probabilities for a given binomial distribution, by calculation and from tables

  2. When to use the binomial distribution • Independent variables

  3. Pascal’s Triangle (a+b)n 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 10 ways to get to the 3rd position numbering each of the terms from 0 to 5. this can also be calculated by using nCr button on your calculator 5C2=10

  4. Pascal’s Triangle (a+b)n 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

  5. A coin is tossed 7 times. Find the probability of getting exactly 3 heads. We could do Pascal's triangle or we could calculate: 7C3 x (P(H))7 The probability of getting a head is ½

  6. TASK • Exercise A Page 61

  7. Unequal Probabilities • A dice is rolled 5 times • What is the probability it will show 6 exactly 3 times? P(6’)=5/6 P(6)=1/6

  8. Task / Homework • Exercise B Page 62

  9. The Binomial distribution is all about success and failure. When to use the Binomial Distribution • A fixed number of trials • Only two outcomes • (true, false; heads tails; girl,boy; six, not six …..) • Each trial is independent IF the random variable X has Binomial distribution, then we write X ̴ B(n,p)

  10. Sometimes you have to use the Binomial Formula

  11. Eggs are packed in boxes of 12. The probability that each egg is broken is 0.35Find the probability in a random box of eggs:there are 4 broken eggs

  12. Task / homework • Exercise C Page 65

  13. Eggs are packed in boxes of 12. The probability that each egg is broken is 0.35Find the probability in a random box of eggs:There are less than 3 broken eggs

  14. USING TABLES of the Binomial distribution An easier way to add up binomial probabilities is to use the cumulative binomial tables Find the probability of getting 3 successes in 6 trials, when n=6 and p=0.3

  15. http://assets.cambridge.org/97805216/05397/excerpt/9780521605397_excerpt.pdfhttp://assets.cambridge.org/97805216/05397/excerpt/9780521605397_excerpt.pdf The probability of getting 3 or fewer successes is found by adding: P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1176 + 0.3026 + 0.3241 + 0.1852 = 0.9295 The probability of getting 3 or fewer successes is found by adding: P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1176 + 0.3026 + 0.3241 + 0.1852 = 0.9295 This is a cumulative probability.

  16. Task / homework • Exercise D page 67

  17. Mean variance and standard deviation • μ = Σxx P(X=x)=mean • This is the description of how to get the mean of a discrete and random variable defined in previous chapter. • The mean of a random variable whos distribution is B(n,p) is given as: • μ =np

  18. Mean, variance & standard deviation • σ²=Σx² x P(X=x) - μ² • is the definition of variance, from the last chapter of a discrete random variable. • The variance of a random variable whose distribution is B(n,p) • σ²= np(1-p) • σ=

  19. TASK / HOMEWORK • Exercise E • Mixed Questions • Test Your self

More Related