AP Statistics / Mr. Hansen 1/27/2003

Name: ________________________

Random Variable Mini-Worksheet

You are given a 6-sided die and are told that the die is loaded in such a way that while the numbers 1, 3, 4, and 6 are equally likely to turn up, the numbers 2 and 5 are three times as likely to turn up as any of the other numbers.

1.	The die is rolled once, and the observed outcome (x) is recorded. Note that x is just a data point, not a r.v. Define X = _____________________________. Make a table that shows all possible values for X and the probability (pi) for each.
2.	Compute the mean and s.d. of X. Use correct notation, and show your work.
3.	Let event A = the number rolled is prime, and let event B = the number rolled is even.
(a)	Are A and B disjoint? Explain.
(b)	Are A and B independent? Explain. If possible, try using more than one way of arriving at your answer.
(c)	Compute P(A | B) and P(B | A) if you have not already done so.