Week 5 Lecture for the Week 5 Quiz

B Heard

Lecture for Week 5 QuizStatistics For Decision

Making

Not to be used, posted, etc. without my expressed permission. B Heard

Your Week 5 Quiz is on material covered in Weeks 3 and 4

Your Week 7 Quiz is on material covered in Weeks 5 and 6

Your Final Exam is comprehensive covering the material in the three prior quizzes plus the material covered in Week 7

Your best approach for preparing for the quizzes should be the Practice Questions offered in the live lecture each week we have a quiz.

Week 5 Quiz


Week 5 Quiz

Let’s look at some questions….


How many ways can a committee of 4 be chosen from 20 people?

Week 5 Quiz


How many ways can a committee of 4 be chosen from 20 people?

This would be a combination because “order” doesn’t matter, so there would be 4845 different ways.

Week 5 Quiz


How many ways can a committee of 4 be chosen from 20 people if they have distinct positions (i.e. President, Secretary, Treasurer, and Vice-President)?

Week 5 Quiz


How many ways can a committee of 4 be chosen from 20 people if they have distinct positions (i.e. President, Secretary, Treasurer, and Vice-President)?

This would be a permutation because “order” does matter, so there would be 116280.

Week 5 Quiz


What values can a probability be?

Week 5 Quiz


What values can a probability be?

Anything between 0 and +1 (NOTHING ELSE). That also means from 0% to 100%, and any positive fraction where the numerator is smaller than the denominator.

Week 5 Quiz


List the sample space of the teams in the 2010 Super Bowl.

Week 5 Quiz


Week 5 Quiz


List the sample space of the teams in the 2010 Super Bowl.

{Colts, Saints}

Other Examples, Gears in my car {P, D, 2nd, Low, R, N}, Numbers on a clock {1,2,3,4,5,6,7,8,9,10,11,12}, Different weeks in our term {1,2,3,4,5,6,7,8}, Grades for the Course {A,B,C,D,F}, Standard Light Switch {On, Off}, etc.

Week 5 Quiz


What is the probability of drawing a 7 from a deck of cards? And what is the probability of a second card being an Ace or King if the first was a 7? (without replacement)

Week 5 Quiz


What is the probability of drawing a 7 from a deck of cards? And what is the probability of a second card being an Ace or King if the first was a 7?

What is the probability of drawing a 7 from a deck of cards? 4/52 or 1/13 And what is the probability of a second card being an Ace or King if the first was a 7? (without replacement)There are 8 Aces and Kings left, but only 51 cards to draw from so it would be 8/51

Week 5 Quiz


What is the probability of drawing a 6, 7, or 8 from a deck of cards? What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 7, or 8? (without replacement)

Week 5 Quiz


What is the probability of drawing a 6, 7, or 8 from a deck of cards? What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 7, or 8?

What is the probability of drawing a 6, 7, or 8 from a deck of cards? There would be 12 of them so 12/52 or 3/13 What is the probability of a second card drawn being a 6, 7, or 8 if the first was a 6, 7, or 8? (without replacement)There would be 11 left and only 51 cards to draw from so it would be 11/51

If there are 13 word documents and 27 excel documents in a folder, and one is randomly drawn, what is the probability of drawing a word document?

Week 5 Quiz


If there are 13 word documents and 27 excel documents in a folder, and one is randomly drawn, what is the probability of drawing a word document?

13/ (13+27) = 13/40

Week 5 Quiz


FactorialsAnswer the following: 4! 3! * 0! 2! /0!

(0!*3!)/4!

Week 5 Quiz


! !!

FactorialsAnswer the following: Remember that the factorial sign means x! = x * x-1 *

x-2 * … 1, so4! = 4*3*2*1 = 24 3! * 0! = (3*2*1) * 1 = 6 (remember 0! is ALWAYS = 1) 2! /0! = (2*1)/1 = 2 (remember 0! is ALWAYS = 1)

(0!*3!)/4! = (1*3*2*1)/(4*3*2*1) = 1/4 (remember 0! is ALWAYS = 1)

Week 5 Quiz


Week 5 Quiz


Decide whether the following experiments would be Binomials, Poissons, or neither. 1. You test 6 different types of batteries. The random variable

represents the battery that is last longest. Past experience is that 30% of the time it is the third of the six types.

2. You observe a stop sign for 4 hours. The random variable represents the number of cars that either completely stopped or didn’t. Historically 65% of cars come to a complete stop.

3. A cab company averages three pickups per hour. We're interested in knowing the probability that in a randomly selected hour they will get one pickup.

4. A company ships computer components in boxes that contain 20 items. We want to know the probability that the 2nd item removed will be defective.

Week 5 Quiz


1. You test 6 different types of batteries. The random variable represents the battery that is last longest. Past experience is that 30% of the time it is the third of the six types. Neither, because we are testing 6 different types (it’s not a yes/no, good/bad, two decision type situation)

2. You observe a stop sign for 4 hours. The random variable represents the number of cars that either completely stopped or didn’t. Historically 65% of cars come to a complete stop. Binomial, probability given in percentage. For this to be Poisson it would say something like on average 42 cars stop at the stop sign every hour, we want to know the probability of exactly 32 stopping, or more than 45 stopping, etc. – the probability (%) was a tip off that it was binomial

3. A cab company averages three pickups per hour. We're interested in knowing the probability that in a randomly selected hour they will get one pickup. Poisson, as per the previous question’s answer we are interested in finding out the probability of 1 pickup.

4. A company ships computer components in boxes that contain 20 items. We want to know the probability that the 2nd item removed will be defective. Neither, we don’t have a probability to start with (Binomial), or an average number of defects (Poisson).

Week 5 Quiz


If X = {1, 5, 9, 12} and P(1) = .3, P(5) = .3, P(9) = .2, and P(12) = .2, can we call it a random variable?

Week 5 Quiz


If X = {1, 5, 9, 12} and P(1) = .3, P(5) = .3, P(9) = .2, and P(12) = .2, can we call it a random variable?

Yes, the sum of the probabilities = (.3+.3+.2+.2) = 1 and they are all between 0 and 1.

Find P(X < 14) for this random variable. X = {1, 5, 7, 13, 15}. P(1) = P(5) = P(7) = P(13) = P(15).

Week 5 Quiz


Find P(X < 14) for this random variable. X = {1, 5, 7, 13, 15}. P(1) = P(5) = P(7) = P(13) = P(15).

Since P(1) = P(5) = P(7) = P(13) = P(15) they must add up to 1 therefore the probability for each must be 1/5 since there are five so it is 0.20

then P(x < 14) = P(1) + P(5) + P(7) + P(13) = 0.20 + 0.20 + 0.20 + 0.20 = 0.80

Week 5 Quiz


If X = {-1, 0, 3, 8} and P(-1) = .3, P(0) = .1, P(3) = .3, and P(8) = .3, can we call it a random variable?

Week 5 Quiz


If X = {-1, 0, 3, 8} and P(-1) = .3, P(0) = .1, P(3) = .3, and P(8) = .3, can we call it a random variable?

Do the probabilities add up to one? .3 + .1 + .3 +. 3 = 1 So yes it is (also note that those probabilities have to be between 0 and 1.)

Week 5 Quiz


We have a binomial experiment with p = .6 and n = 3. Set up the probability distribution and compute the mean, variance, and standard deviation.

Week 5 Quiz


Templates for Binomial and Poisson

http://highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html

I will post this in the chat area of the lecture

Week 5 Quiz

See Excel Spreadsheet picture that follows.

X = {0, 1, 2, 3}P(X = 0) = 0.06 P(X = 1) = .29 P(X = 2) = .43

P(X = 3) = .22E(X) = n*p = 3 * .6 = 1.8 (listed as mean in provided excel spreadsheet picture that follows) V(X) = n*p*q, q = 1 - p = 1 - .6 = .4 V(X) = 3*.6*.4 = .72 (listed as variance in provided excel spreadsheet)standard deviation = sqrt(variance) = sqrt(.72) = .85 (listed as stdev in provided excel spreadsheet picture that follows)

Week 5 Quiz


Week 5 Quiz


Week 5 QuizWe have a Poisson with mu = 3. Find P(X = 4), find P(X < 4), find P(X >= 4), compute the mean, variance, and standard deviation.

Week 5 QuizSee Excel Spreadsheet attached to follow on post.P(X = 4) = 0.168 (see picture of excel spreadsheet yellow block)P(X < 4) = 0.647 (see picture of excel spreadsheet green block)P(X >=4) = 0.353 (see picture of excel spreadsheet gray block)mean = variance = 3 (see picture of excel spreadsheet)standard deviation = sqrt(variance) = 1.73 (see picture of excel spreadsheet)


Week 5 Quiz

We have the random variable X = {5,10} with P(5) = .6 and P(10) = .4. Find E(X).

Week 5 Quiz


http://images.google.com/imgres?imgurl=http://focus.aps.org/files/focus/v19/st18/marbles_BIG.jpg&imgrefurl=http://focus.aps.org/story/v19/st18&h=482&w=724&sz=51&hl=en&start=9&um=1&usg=__I2i2WvGyphmck5c5bNo5ydMC54k=&tbnid=QMJjEiqbsfu5sM:&tbnh=93&tbnw=140&prev=/images?q=marbles&um=1&hl=en

We have the random variable X = {5,10} with P(5) = .6 and P(10) = .4. Find E(X).

E(X) = sum of (x*P(X)) = 5*P(5) + 10*P(10) = 5*.6 + 10*.4 = 3.0 + 4.0 = 7.0

Week 5 Quiz


Continuous or discrete?

1. The amount of oil in your car’s engine?2. The number of cans of coke in your

refrigerator?3. Your son’s weight?4. The number of cousins you have?5. The amount of butter in your butter dish?6. The number of classes you have taken and

received credit for?

Week 5 Quiz


Week 5 QuizContinuous or discrete?1. The amount of oil in your car’s engine?

Continuous2. The number of cans of coke in your

refrigerator? Discrete3. Your son’s weight? Continuous4. The number of cousins you have? Discrete5. The amount of butter in your butter dish?

Continuous6. The number of classes you have taken and

received credit for? DiscreteNot to be used, posted, etc. without my expressed permission. B Heard

What is the probability the student is a 1st Grader?

What is the probability the student is a 2nd Grade boy?

What is the probability that the student is a girl given that she is in the second grade?


What is the probability the student is a 1st Grader? 25/50 or ½ (0.5)

What is the probability the student is a 2nd Grade boy? (8/50 or 4/25 (0.16)

What is the probability that the student is a girl given that she is in the second grade? 17/25 (0.68)


Week 5 Quiz

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Week 5 Lecture for the Week 5 Quiz