We have previously discussed the probability experiment of rolling two 6-sided dice and its sample space. Now we can look at random variables based on this probability experiment. A natural random variable to consider is:

X = sum of the two dice

You will construct the probability distribution of this random variable. For reference, I wrote out the sample space and set up the probability distribution of X; see the snapshot below.

It will be a exam exercise to complete the probability distribution (i.e., fill in the entries in the table below) and to graph the probability distribution (i.e., as a histogram):

I just uploaded the snapshot in this post as a pdf to Files, in case that’s easier to read. We went over this at the end of the Blackboard class session just now.

I didn’t write up a separate post on what we covered last Wednesday (April 22) during the Blackboard Collaborate session, but thought I’d post some notes on what we covered:

–during the 1st 40 minutes, we went over another exercise on HW8 (the written HW on permutations and combinations, which is due by the end of the day tomorrow (Monday April 27), as a Blackboard submission)

–for the last hour, we continued to go over discrete random variables and probability distributions. In particular, we went over one of the examples on the class outline, and then we started to go over the exercise I outlined in the post above: constructing the probability distribution for the random variable

X = “the sum of two 6-sided dice”

That homework exercise will be due on a date TBA, along with some additional exercises on random variables and probability distributions.

For now, please finish HW7 (the WebWork set on conditional probability) and HW8.

If you’ve finished both of those, you can read the post I wrote up on Friday about Bayes’ Theorem, which is an important application of conditional probability:

https://openlab.citytech.cuny.edu/math1372-ganguli-spring2020/2020/04/24/intro-to-bayes-theorem/

We will have a Blackboard session at the regularly scheduled times this week, where we will continue with some additional topics on random variables and probability distributions (expected value and standard deviation of RVs tomorrow, followed by binomial random variables on Wednesday).