Common Core Standards: Math
3. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
Students should be able to find expected values and distinguish random variables already. Now, they should do all that while standing on their heads and juggling coconuts.
Well, maybe not. But this standard does ask students to do a little bit more than know what values are and how to find them. Students should think through the problem and develop their own theoretical probabilities (instead of being spoon-fed the theoretical probabilities of a question).
This means that students should be able to distinguish when events have equal probabilities or differing ones, as well as which are associated with which. They should be able to figure out what they're being asked to find (the expected value or the probability or the actual average) and calculate it accordingly.
Yes, this involves using both P(X = a) = nCa • pa • qn – a and E(x) = x1p1 + x2p2 + … + xipi. Tell your students not to get too excited.
Once they have achieved the ability to understand theoretical probabilities, they must then apply the lessons of the previous two standards to come up with expected value and probability distributions. The next step after that is coconuts and an impeccable sense of balance (and a comprehensive health insurance plan).