Reading Assignment #9 - Due 2/13/12

Here's your next reading assignment. Read Sections 3.2 and 3.4 in your textbook and answer the following questions by 8 a.m., Monday, February 13th. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

  1. Consider the normal probability plot seen below. Looking at the plot, would you say that the data come from a normally distributed population? If not, how would the histogram for these data vary from that of a normal histogram?  (You can click on the image below to see a larger version.)
  2. Consider the following experiment: On a Friday night, a highway patrol officer sets up a roadblock and stops 100 drivers. A given driver is considered a success if he or she is wearing a seat belt; the driver is considered a failure otherwise. Can we consider this experiment a binomial experiment? Why or why not?
  3. What's one question you have about the reading?

Midterm Exam #1 on Wednesday

Thanks for your responses (via clickers and email) to my question about moving the first midterm exam from Wednesday to Friday next week. I'm going to leave it on Wednesday. I know this disappoints some of you, but, as I said during class, I'm hesitant to move the date of an exam. A few of you let me know about travel plans you made so as to avoid the Wednesday exam, based on the schedule I shared at the beginning of the semester. Changing the exam date now seems unfair to those students.

I hope to have more info about the exam for you soon. For now, know that it will cover the material associated with Chapters 1 and 2 in our textbook.

Reading Assignment #8 - Due 2/8/12

Here's your next reading assignment. Read Sections 3.1 (and 2.5, if you haven't already) in your textbook and answer the following questions by 8 a.m., Wednesday, February 8th. Be sure to login to the blog before leaving your answers in the comment section below.

  1. In the normal probability table at the back of your book (pages 362-363), the value 0.0618 appears at the intersection of the row labeled -1.5 and the column labeled 0.04. In your own words, describe the meaning of this entry in the table.
  2. Consider the random variable X = the weight in pounds of a randomly selected newborn baby born in the United States during 2011. Suppose that X can be modeled with a normal distribution with mean 7.57 and standard deviation 1.06.  What is the probability that the birth weight of a randomly selected baby exceeds 9 pounds?
  3. For the random variable in question 2, if the standard deviation were 1.26 instead, how would that change the shape of the graph of the probability distribution function of X?
  4. What's one question you have about the reading?

More on the Monty Hall Problem

Once again, here's the Monty Hall problem:

Monty Hall offers you a choice of three doors.  Behind two are goats, and behind the other door is a brand new car.  After you make your choice, Monty opens one of the doors you didn’t choose to reveal a goat, and offers you the chance to switch your choice to the one remaining.  What should you do?  (Assume Monty knows where the car is and always opens a door with a goat after the contestant chooses.)

  1. Switch
  2. Stay
  3. It doesn't matter.

Many people think that once Monty opens a door to reveal a goat, that with only two doors remaining, their odds of winning the car are 50-50.  That explains why many people think it doesn't matter if you stay or switch.  Some people think that perhaps Monty is trying to talk them out of sticking with their original door because it contains the car.  These people are likely to think that staying with their first choice gives them better than 50-50 odds.

However, the correct way to think about this problem is that you had a 1/3 chance of guessing right on your first try. After Monty opens a door and reveals a goat, there's still a 1/3 chance that you were right, which means there's still a 2/3 chance that you were wrong. Before Monty opened that door, that 2/3 chance that the car was not behind your door was split between two doors. Now, however, there's a 2/3 chance that the car is behind the remaining door that you didn't choose. So you should switch. On average, you would expect to win a car 2/3 of the time if you switch.

Here's the tree diagram I showed briefly in class. It helps to model this random process in something of a chronological order. First, the car is placed behind one of the three doors randomly, with each door being equally likely.  Then, you select your door, again with each door being equally likely. Then, Monty opens one of the other doors to reveal a goat. (It's important that Monty knows where the goats are here! Otherwise you get a different tree diagram.) When you look at the outcomes, not all are equally likely because Monty's choices are limited in some cases. Of all the outcomes, weighted by their respective probabilities, your choice of door was correct only 1/3 of the time. Thus, switching doors is the better strategy.

Here's another way to think about this: When you picked your door, you had a 1/3 chance of picking the door with the car. When Monty opens a door to reveal a goat, he's giving you more information than you had originally. (Again, this assumes that Monty knows where the goats are.) When you get more information, you can improve on your initial 1/3 chance of winning. That's why this is a conditional probability problem: Given information about one event (that one of the doors you didn't choose has a goat behind it), the probability of another event (that you chose correctly) changes.

To hear what Monty Hall himself had to say about this problem, check out this New York Times interview. One thing made clear in that interview is that Monty did indeed know where the goats were. But, in contrast to the problem as I stated it above, he wasn't required to always open a second door and offer contestants the chance to switch. If the contestant chose a door with a goat, Monty didn't have to make any deals!

Image: "Goats Only," by me

Problem Set #2 - Due 2/8/12

Here's your second problem set, in Word and PDF formats. It's due at the start of class on Wednesday, February 8th. Remember, you can collaborate on your problem sets; just identify those with whom you worked when you turn in your problem set. Also, don't forget about our office hours, including three on Tuesday.

Clarification: On the last problem, I used the variable "EQ_MAG_MW" for the magnitude data.

Let's Make a Deal

Here's the Monty Hall Problem, as I posed it at the end of class today:

Monty Hall offers you a choice of three doors.  Behind two are goats, and behind the other door is a brand new car.  After you make your choice, Monty opens one of the doors you didn’t choose to reveal a goat, and offers you the chance to switch your choice to the one remaining.  What should you do?  (Assume Monty knows where the car is and always opens a door with a goat after the contestant chooses.)

  1. Switch
  2. Stay
  3. It doesn't matter.

Feel free to try and figure it out between now and Friday!

Image via Wikimedia Commons

Reading Assignment #7 - Due 2/3/12

Here's your next reading assignment. Read Sections 2.3.7 and 2.4 in your textbook and answer the following questions by 8 a.m., Friday, February 3rd. Be sure to login to the blog before leaving your answers in the comment section below.

  1. Given what you know about conditional probability, what do you make of this statement? "For life to occur on Earth as we know it, the Earth's temperature had to be just right. Since the odds of an Earth-life planet orbiting a Sun-like star at just the right distance to produce Earth-like temperatures are astronomical, the presence of life on Earth is somehow special."
  2. What's one question you have about the reading?