Homework exercises will be assigned weekly and posted below. You are expected to know how to do all of the exercises presented. Online help is available through Piazza, an online forum. See the help page for more details.
Chapter 1: Theoretical Exercises (pg 17ff): 8 (see note below), 13, 17 (see note below)
Note: For theoretical exercise #8, interpret "prove" as "give a convincing argument." For theoretical exercise #17, interpret "combinatorial argument" as "explain why you expect this to be true by a counting example, rather than just the mathematical algebra."
Note: For #5 and #7, when the book says, "what are the possible outcomes..." for a particular random variable, I want you to read it as, "what is the state space of ..." that particular random variable.
Note: For #40, you can likely answer this without the "technology" of random variables; however, try and use the random variable technology to get used to it. In particular, if X is the (random variable giving the) number of correct answers the student gets while guessing, then convince yourself that X = Bin(n,p) for a good choice of n and a good choice of p.
For both #15 and #17, leave your answer in terms of Φ. For the second question in #21, it is asking for you to condition on the event that the height is ≥ 6 feet.
The CDF Φ of a standard normal random variable is invertible on the range (0,1). That is, if for some 0 < y < 1 you have an expression of the form Φ(x) = y, you can solve for x by x = Φ^{-1}(y) (where Φ^{-1} is the inverse of Φ, not 1/Φ). Therefore, if you don't want to use the table of values for Problems #18 and #19, you can leave your answer in terms of the inverse Φ^{-1}.
For Theoretical Exercise #9, when the book says "show," what I want you to do is to draw a sketch of the density of Z and convince yourself that the equalities are true by shading in the appropriate areas.