Reference no: EM131092618
1. The following data comes from the 2011 Behavioral Risk Factor Surveillance System (BRFSS) survey, which is run by the Centers for Disease Control (CDC). This is a joint probability table for the proportions of survey respondents who smoke and who have had heart attacks.
Answer the following questions:
(a) What is the proportion of people who smoke?
(b) What is the proportion of people who have had a heart attack?
(c) If a person is a smoker, are they more likely to have had a heart attack than someone who is not a smoker? Hint: Be careful what this question is asking!
(d) If someone tells you that they have had a heart attack, what is the probability that they are also a smoker?
(e) Is smoking independent of having a heart attack?
(f) Define Bernoulli random variables, S = 0 (non-smoker), S = 1 (smoker), and H = 0 (no heart attack), H = 1 (heart attack). What is Cov(S, H)?
(g) What is ρ(S, H)?
2. Let k be some constant number, and consider continuous random variables X and Y with joint pdf 
(a) Find k.
(b) What is the joint probability P
(c) What is the marginal pdf fX(x)?
(d) What is the marginal pdf fY (y)?
(e) What is the conditional probability P(x≤Π/4 ly=Π/4)
(f) Are X and Y independent? Explain why or why not.
(g) What is Cov(X, Y )?
(h) What is ρ(X, Y )?
3. A polling station in Salt Lake City has 50 registered Republicans and 50 registered Democrats. After 4 people show up to vote, let R be the number of Republicans and D be the number of Democrats that have voted.
(a) Compute and list all the entries of the joint probability table P(R = a, D = b) that are non-zero.
(b) What is Cov(R, D)?
(c) What is ρ(R, D)?
Hint: These computations may seem daunting, but the final answers should come out to be simple numbers. You can use a calculator of course, but don’t just give the final answer –show your work!
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