Topics:
• More on probability distribution functions on sample spaces:
As a consequence of the axioms and theorems from last time, We can (and usually will) define a probability distribution on a sample space S by assigning a probability to each outcome in S, in such a way that every probability is non-negative and they all add up to 1 (= the probability of S).
Then we have the Theorem:
For any event A in S, P(A) is the sum of the probabilities of the outcomes in A.
• Conditional probability
The notes I showed on the screen in class are here:
Math2501ConditionalProbabilityIndependence
We only went through basically the first page of those notes. I’ll write more notes on the other examples here when I have time.
Homework:
• Be on the lookout for an email invitation to join our Datacamp group, coming soon to whatever email address Blackboard has for you!
• If you have not already joined Piazza: Look for the invitation to join our Piazza discussion board, and join by following the link. The invitation has been sent to whatever email address you have in Blackboard, and it will be from “The Piazza Team”. Or you can go directly to Piazza here and join using your City Tech email address. We will be using the discussion board as a way to ask questions about the homework or the material discussed in class, and also you will be submitting some of your R assignments via Piazza.
• Do the following from the textbook: (I have posted a copy of these problems over on Piazza on the “Resources” tab)
P. 39: #2.4.1, 2.4.2, 2.4.5, 2.4.12, 2.4.13, 2.4.14, 2.4.15
Notes:
In problem 2.4.2, make use of the definition of the conditional probabilities P(A|B) and P(B|A)
In problem 2.4.5, before doing it, you should think about why the four birth orders in Example 2.42 should be considered to be equally likely (as we did) – or should they?
• Monday 12 February is a holiday (no classes meet).
• There will be a Quiz on Wednesday. The question will be a randomly selected homework problem from today’s assignments.
Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!
Note on my schedule: for the time being, I will only be able to be online to read and reply to emails at certain times of the day. (It is possible that I may be online at other times but I cannot guarantee it.) The times are roughly:
Monday – Friday early morning
Monday-Thursday around 2:30-3:00 PM
Sunday-Thursday evenings around 9-10 PM
Please be aware of this if you need to contact me by email. Thanks.
