Open course ware

PHILIP GREENSPUN: So remember, as VFR pilots, you're actually going to be doing stuff that is in some ways more challenging than what airline pilots do, because you're always trying to keep clearances from clouds that the IFR pilots don't care about. And if you're flying a low performance airplane, you're also dealing with flying through the weather instead of just going on top of it. So while you're the VFR only pilot, these non-local flights, really pay attention to weather. Airspace, go and study this a little bit before the exam. Here are the different kinds. Remember Class A is up high. You need an instrument clearance. Class B is around the biggest airports. Class Charlie's around Manchester, New Hampshire. And D is for Hanscom. And E is everywhere else. OK. The goal for the basic VFR weather minimums is to make sure that an IFR plane coming out of the cloud has time to see and avoid you, because the air traffic controller's job is to...

PROFESSOR: Now you may remember a discussion of the birthday paradox, which says that if you have a group of 27 random people. The probability is almost 2/3 that two of them are going to have a matching birthday, even though there are 365 birthdays in the year. You might sloppily think that with 27 people there'd only be a 27 out of 365, or some chance like that. It's actually 2/3. And by the time you get to a class of 110-- which is what we have data for and we're going to be looking at-- it turns out that the odds are almost 3/4 of a million to one that you'll have a couple of people with matching birthdays. So let's look at the matching birthday problem a little bit more today. And the reason we're looking at it is because it's a lovely example where there really is pairwise independence, and not mutual independence. So it's reinforcing the key idea behind the additivity of variance, and the pairwise independent sampling theorem. We'...

Remember that in our previous video, we created four new variables, HighSodium, HighFat, HighCarbs, and HighProtein. Now in this video, we will try to understand our data and the relationships between our variables better, using the table and tapply functions. To figure out how many foods have higher sodium level than average, we want to look at the HighSodium variable and count the foods that have values 1. We can do this using the table function, and give it as an input the HighSodium vector. Now pressing Enter, we obtain the following information. Most of the foods in our data set, and precisely 4,800 of them, have lower sodium than average, and we have 2090 foods that have higher sodium content than average. Now let's see how many foods have both high sodium and high fat. Well, to do this we can also use the table function, but instead of giving it one input, now we can give it two inputs. So let's go back using the Up arrow, and now have the first input being...