Write the names of the students at your table:
Consider an experiment described by “A student takes a Data Science exam”, whose sample is the possible letter grades \(\{A, B, C, D, F\}\) the student could receive. Write down two examples of events; one of your examples should not also be a single outcome.
Write down a valid set of probabilities of each of the possible outcomes of the experiment described above.
Write down the value of a random variable \(G\) that represents the GPA value associated with each outcome.
Using your probabilities from above, calculate the expected value of \(G\).
Describe the rolling of a fair six-sided die using the terminology of probability.
Let \(V\) be a random variable euqal to the number on the die itself; find its expected value.
Do the same as above for a roll of two fair six-sided dice, and calculate the expected value of the random variable that is the sum of the numbers that the two dice land on.
Draw the PDF for a loaded five-sided die that comes up 1 with probability 0.6 and has an equal chance of each the remaining four faces.
As variability measures, the standard deviation and variance are closely related to the mean, meaning that they are likely to be sensitive to outliers just as the mean is. Can you think of a way to measure variability that might be more robust to outliers?