For the notes from Monday’s class, see this post.

Homework:

• Don’t forget to keep working on the R assignments in Datacamp! You can keep working on them even after the due date:  just don’t let them pile up until the end of the semester!

• Make sure to do the problems assigned last time.

• For the experiment “Flip a coin until heads shows”, if the coin is unbalanced so that $P(H) = \frac{3}{5}$, find the probability distribution function for the random variable X = the number of tails, and show that the probabilities add up to 1.

Note: The sum of the geometric series $\displaystyle \sum_{k=0}^{\infty}ar^{k} = \frac{a}{1-r}$ if $|r| < 1$

• Find the probability distribution function for the random variable Y = the number of even numbers that show on the dice, for the experiment “roll two balanced dice”

• There will be a Quiz on Wednesday. It will be based on one of the homework problems mentioned above (including from last time).

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!

Topics:

• Counting permutations when there are indistinguishable elements

• Discrete Random Variables

Here are my notes on discrete random variables:

MAT2572RVsAndTheirPDsNotesDiscreteCase

Homework will be in a separate post.

If you are defining a random variable, the important thing is that you should be able to look at any outcome in the sample space and say what  number goes with that outcome.

I could  define a different random variable for the example of rolling two balanced dice, as follows:

Y = the number of even numbers that show on the dice.

Then for the outcome (1,1), Y=0, and for the outcome (2,3), Y=1. The value of Y depends on the outcome of the random experiment.

The possible values of Y are 0, 1, and 2

Exercise: find the pdf for Y

From section 2.6: