A polling station in Salt Lake City has 50 registered Republicans and 50 registe

Question

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 row(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!

Explanation / Answer

There are 50 R voters and 50 D voters. 4 people show up to vote. Among them number of registered R or D voters may be 0,1,2,3 or 4. The following table gives the joint probability P(R=a; D=b) for all possible combinations:

D R: 0 1 2 3 4

0 50C4/100C4 =0.0587

1 50C1*50C3/100C4=0.2499

2 50C2*50C2/100C4=0.3828

3 50C3*50C1/100C4=0.2499

4 50C4/100C4 =0.0587

To calculate the Cov(R,D), first we calculate the mean of R and D. E(D) = E(R) = 0.2499 X 1+ 0.3828 X 2 + 0.2499 X 3 + 0.0587 X 4 = 2.

Cov(R,D) = 0.2499 X 1 X 3 + 0.3828 X 2 X 2 + 0.2499 X 3 X 1 - (2)^2 = 3.0306 - 4 = -0.9694.

(c) For part C, it is not clear what it actually means.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.