You do not need to bring your book to class. However, you do need to bring your TI-84+/83+ calculator.
Lecture 3
Comments
1. You do not need to bring your book to class. However, you do need to bring your TI-84+/83+ calculator.
2. The book asks you to use the Binomial Table for the Binomial distribution problems. Ignore this and use the binompdf() function instead.
Homework
1. An experiment consists of rolling a die once. The experiment is interested in the event: an even numbered face comes up.
(a) How would you de ne a random variable so that it would be Bernoulli?
(b) Is it necessary for the die to be fair? Explain.
(c) If the die is fair, what is p?
(d) If the die is biased such that an even face is three times as likely to come up as an odd face, what is p? (4.3.1)
2. Suppose two fair dice are rolled once. De ne a random variable of your choosing so that it is Bernoulli. (4.3.3)
3. A batch of 1,000 light bulbs is tested. The person doing the testing wants to know the number of defective light bulbs. Let the random variable of interest be denoted by X. The range of X is f0; 1g where `0′ denotes the light bulb works and `1′ denotes the light bulb is defective. Explain how X meets the Bernoulli de nition. (4.3.5)
4. A basketball player shoots free throws. The number of free throws made is recorded. De ne a random variable so that it is Bernoulli. Explain. (4.3.7)
5. A manufacturer of light switches produces defective light switches with probability 0.10. Sup- pose you buy a package of 15 light switches. (4.4.2, 4.4.3, 4.4.7, 4.4.9, 4.4.13)
(a) Let X = number of defective switches. Give the range of X.
(b) Fill the blanks: X e B( , ).
(c) What is the probability that when testing 15 switches the following outcome occurs? (Note: D
represents a defective switch; N represents a non-defective switch.)
Switch Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Outcome D N D N N N N N N N N N N N N
(d) Find P(X 10). What probability does this represent?
(e) On average, how many defective light switches will be found in a package of 15?
6. Julia makes free throws with 60% accuracy.
(a) If X = number of free throws made in n attempts and = 18, what is n?
(b) What is the probability that in 20 attempts Julia will make at least 15 free throws?
(c) What is the probability that Julia will make the free throw on the very rst attempt?
7. A sales representative for a tire manufacturer claims that her steel-belted radials will last at least 40,000 miles. A tire dealer decides to check this claim by testing 20 randomly chosen tires. If 75% or more of the 20 tires tested last at least 40,000 miles, the dealer will purchase tires from the sales representative.
(a) In extensive tests, the tire manufacturer establishes that 90% of the manufactured tires last at least 40,000 miles. Is this a binomial situation? Explain.
(b) Under the conditions of part(a), what is the probability that the tire dealer will purchase tires from the sales representative?
(c) Instead, suppose the tire manufacturer establishes that 70% of the manufactured tires last at least 40,000 miles. What is the probability that the tire dealer will purchase tires from the sales representative? Explain why this probability is smaller than the probability in part (b)
8. Your local TV weather person produces weather forecasts with 60% accuracy. Assume that the weather forecast for consecutive days is independent.
(a) What is the probability that, over the next two days, the forecaster is correct on both days?
(b) What is the probability that, over the next two days, the forecaster is correct on one day and wrong on the other?
(c) What is the probability that out of a ve-day week (Monday through Friday), the forecaster is correct for the rst time on Friday?
(d) What is the probability that the forecaster will be correct in at least 5 of the next 8 weather forecasts?
(e) What is the expected number of incorrect forecasts out of the next 100 forecasts?
(f) What is the probability that out of a sequence of 5 consecutive days the forecaster will give a correct forecast on the fth day if the forecaster has already given correct forecasts on the four previous days?
9. A fair die is rolled until a `5′ or `6′ comes up.
(a) De ne the random variable X.
(b) What constitutes a success”? What constitutes a failure”?
(c) Fill in the blank: Xe G( ).
(d) What is the probability that the rst `5′ or `6′ comes up on the 4th roll of the die?
10. Let X e G(0.3) and Y e G(0.4).
(a) True or False: P(Y 4) < P(X 4). Explain without computing the probabilities.
(b) True or False: frange of Xg = frange of Y g. Explain.
11. A computerized stock trading program recommends stocks that show a pro t with probability = 0.60. The computer is programmed to recommend one stock per trading day.
(a) Let X = number of stocks recommended by the computer program until the rst pro table stock. Is the distribution of X Geometric?
(b) Let W = number of pro table stocks recommended by the computer program over the next 200 trading days. Is the distribution of W Geometric? Explain.
(c) Find the probability of at least three pro table stock recommendations over the next ve trading days.
(d) Find the expected number of pro table stock recommendations over the next 200 trading days
Collepals.com Plagiarism Free Papers
Are you looking for custom essay writing service or even dissertation writing services? Just request for our write my paper service, and we'll match you with the best essay writer in your subject! With an exceptional team of professional academic experts in a wide range of subjects, we can guarantee you an unrivaled quality of custom-written papers.
Get ZERO PLAGIARISM, HUMAN WRITTEN ESSAYS
Why Hire Collepals.com writers to do your paper?
Quality- We are experienced and have access to ample research materials.
We write plagiarism Free Content
Confidential- We never share or sell your personal information to third parties.
Support-Chat with us today! We are always waiting to answer all your questions.
