Problem Set 8 Hints

For better or for worse, I decided to do this round of hints as a series of videos. Check them out to get some information (and even some picture hints!) on how to solve these questions. There is a hint for every problem except number two, that one was pretty straightforward.

Don't forget to interpret in the context of the problem, use complete sentences, and bring your hot chips inspired dish for the Thanksgiving Iron Chef Competitin tomorrow!! +10 bonus points if you participate!!

http://www.educreations.com/lesson/view/probset8hints1/14020302/?s=aIbFX6&ref=app

http://www.educreations.com/lesson/view/probset8hints3/14020390/?s=MmLbqF&ref=app

http://www.educreations.com/lesson/view/probset8hints4/14020456/?s=9BEMj3&ref=app

http://www.educreations.com/lesson/view/probset8hints5/14020511/?s=8mHmXV&ref=app

Enjoy!

Binomial Distributions

Binomial distributions are discrete distributions where x, the random variable, can either succeed or fail at something. The problem will give you a probability (of success or failure), a number of trials, and how many successes they are looking for.  Your answer will be a probability and should be written in the form p(x = c) where c is the number that you are looking for in the problem.

We made binomial distributions in class today based off of tables and of graphs. Either one conveys the same information. I also discussed how to do this in the calculator. Go to 2nd - vars, then scroll down to binompdf. From there, type in the number of trials, the probability as a decimal between 0 and 1, and the number of successes.

Your answer should be interpreted as:"The binomial probability of getting (number of successes) given (number of trials) and (probability) of success is (your answer)."

Discrete and Uniform Distributions

A distribution is what the data looks like (to put it in very simplified terms). Distributions can either be discrete (exact values) or continuous (infinite decimal values). When we simulate a distribution, the center of the distribution/highest peak becomes known as the expected value of the distribution. This means that, given no other information, we'd expect a random trial to give us that value because it is the most common.

A uniform distribution is one where the probability of any value happening is the same throughout the distribution. Remember that the the probability under a curve (uniform or not) is always equal to 1. We did the following example of a uniform distribution in class on Friday but never quite got around to finishing it. Click on the link below to get the whole video solution to the following question:

"Let x be the time in minutes that a commuter must wait for a public transit train, with the minimum wait time being 0 minutes and the maximum wait time being 20 minutes. Suppose that the writ times are uniformly distributed.
A. Draw a density curve to model the distribution.
B. what is the probability that x is less than 10 minutes?
C.  What is the probability that x is between 7 and 12 minutes?
D.  Find the value of c for which P(x < c) = .9.

http://www.educreations.com/lesson/view/uniform-distribution/13711048/?s=LDKaL9&ref=app

Simulations

We have studied simulations over the past few days - once in the context of goldfish and once in the context of trying to recall as many 3-letter words as possible within a 1-minute time period. Simulations are repeated experiments. We perform simulations to gain insight on what the population distribution looks like. The more simulations we perform, the less variability we have, and the more the sample distribution looks like the population distribution.

When describing a simulation, we always:
1. State the model
2. Define what one trial is, and mention if there is a stopping rule.  Note that the AP exam requires at least 100 trials for a simulation to be large enough
3.  State what is being recorded (I.e. what is the random variable?)
4.  Perform the simulation and collect results
5.  Analyze the results

Review, Tests, and Next Steps

It's been a while since I've posted - so sorry about that guys! A big shout out to everyone who was involved with today's ROTC/band/choir performances at Veteran's Day. You ROCKED - it sounded and looked phenomenal.

Today we just graded the exams in class and talked about open response questions. The good news is that nobody completely bombed the open responses - to an extent, you all had an idea of where the question was taking you. LOVED IT. However, we still need to improve on mastering the use of statistical vocabulary in the context of our answer. I needed to see words like "treatment," and "placebo groups" and "randomization" rather than "that thing that affected the data...." yeah. Be specific!

We're going to start a mini-unit on simulations and expected value, along with some theoretical discussions on distribution shape. We know that the Normal Curve is one type of distribution available - but how many others are out there? To be continued...