DOC PREVIEW
UIUC STAT 400 - 400Ex2_4

This preview shows page 1 out of 4 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 4 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 4 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

STAT 400 Lecture AL1 Examples for 2.4, 2.5 Spring 2015 Dalpiaz Binomial Distribution: 1. The number of trials, n, is fixed. 2. Each trial has two possible outcomes: “success” and “failure”. 3. The probability of “success”, p, is the same from trial to trial. 4. The trials are independent. 5. X = number of "successes" in n independent trials. Then ( ) ( ) kn k kn k p pkCnp pknk −−⋅⋅=−−⋅⋅==11P)( X, where k = 0, 1, … , n. E ( X ) = n ⋅ p Var ( X ) = n ⋅ p ⋅ ( 1 – p ) SD ( X ) = ( ) p pn −⋅⋅ 1 1. Bart Simpson takes a multiple choice exam in his Statistics 101 class. The exam has 15 questions, each has 5 possible answers, only one of which is correct. Bart did not study for the exam, so he guesses independently on every question. Let X denote the number of questions that Bart gets right. a) Is it appropriate to use Binomial model for this problem? b) What is the expected number of questions that Bart would get right? c) What is the probability that Bart answers exactly 3 questions correctly?d) What is the probability that Bart would get at most 5 of the questions right? e) What is the probability that Bart would get more than half of the questions right (i.e. what is the probability that Bart would get at least 8 of the questions right)? f) Find the probability that Bart answers between 4 and 6 (including both 4 and 6) questions correctly? Binomial Outcome Probability k CDF at k n = 15 0 0.03518437 0 0.03518437 p = 0.20 1 0.13194140 1 0.16712577 2 0.23089744 2 0.39802321 3 0.25013890 3 0.64816210 4 0.18760417 4 0.83576628 5 0.10318229 5 0.93894857 6 0.04299262 6 0.98194119 7 0.01381906 7 0.99576025 8 0.00345476 8 0.99921501 9 0.00067176 9 0.99988677 10 0.00010076 10 0.99998754 11 0.00001145 11 0.99999899 12 0.00000095 12 0.99999994 13 0.00000006 13 1.00000000 14 0.00000000 14 1.00000000 15 0.00000000 EXCEL: =BINOMDIST( k , n , p , 0 ) =BINOMDIST( k , n , p , 1 )2.☺ An automobile salesman thinks that the probability of making a sale is 0.30. If he talks to five customers on a particular day, what is the probability that he will make exactly 2 sales? (Assume independence.) 3.☺ A major oil company has decided to drill independent test wells in the Alaskan wilderness. The probability of any well producing oil is 0.30. Find the probability that the fifth well is the first to produce oil. Geometric Distribution: X = the number of independent trials until the first “success”. Then ( ) ( )ppxxX⋅−−==1 1P, x = 1, 2, 3, … . E ( X ) = p1. Var ( X ) = 21pp−. 4. A slot machine at a casino randomly rewards 15% of the attempts. Assume that all attempts are independent. a) What is the probability that your first reward occurs on your fourth trial? b) What is the probability that your first reward occurs on your seventh trial?c) What is the probability that your get three rewards in ten trials? d) What is the probability that your third reward occurs on your tenth trial? Negative Binomial Distribution: X = the number of independent trials until the k th “success”. Then ( ) ( )kxkX ppkxx−−−−== ⋅⋅ 111P, x = k, k + 1, k + 2, … . E( X ) = pk. V( X ) = ( )2 1ppk−⋅. EXCEL: = NEGBINOMDIST( x – k , k , p ) gives P( X = x ) e) What is the probability that your fourth reward occurs on your fifteenth trial? f) What is the probability that your get four rewards in fifteen


View Full Document

UIUC STAT 400 - 400Ex2_4

Documents in this Course
Variance

Variance

11 pages

Midterm

Midterm

8 pages

Lecture 1

Lecture 1

17 pages

chapter 2

chapter 2

43 pages

chapter 1

chapter 1

45 pages

400Hw01

400Hw01

3 pages

Load more
Download 400Ex2_4
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view 400Ex2_4 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view 400Ex2_4 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?