Penn STAT 101 - STAT 101 Solutions Midterm Exam (2 pages)

Previewing page 1 of 2 page document View the full content.
View Full Document

STAT 101 Solutions Midterm Exam



Previewing page 1 of actual document.

View the full content.
View Full Document
View Full Document

STAT 101 Solutions Midterm Exam

77 views

Lecture Notes


Pages:
2
School:
University of Pennsylvania
Course:
Stat 101 - Introductory Business Statistics.

Unformatted text preview:

Solutions Midterm Exam II Fall 2004 Statistics 101 1 A First compute E XY 1 0 1 2 0 1 3 0 4 0 3 6 0 3 9 0 2 5 1 Hence Cov X Y 5 1 2 2 2 2 0 26 and so Cor X Y 0 26 0 46 0 565 Thus ratings tend to go in the same direction there is a moderate linear relationship between the two ratings B Plainly the expectation will be the same as the original expectation viz 2 2 To compute the standard deviation we use the relationship Var X 2 Y 2 1 4 Var X 1 4 Var Y 1 2 Cov X Y Thus from the first part we have Var X 2 Y 2 1 2 46 1 2 0 26 0 36 Thus SD 0 6 Since there is a positive correlation independence would reduce the overall variance but have no e ect on the mean C First we compute the conditional probabilities P rating k same and these are 0 1 0 6 1 6 0 3 0 6 1 2 and 0 2 0 6 1 3 for k 1 2 3 respectively Hence E rating same 1 1 6 2 1 2 3 1 3 2 16 2 A P X 9 R 10 9 3x2 1000dx 0 271 B i We assume a binomial model Thus X B 100 0 271 and P 20 P100 k n k X k 20 100 k 0 271 0 729 ii We use the central limit theorem p X N 27 1 27 1 0 729 and compute P 20 X P 20 27 1 4 4476 Z P 1 597 Z 0 9452 C i OK integrate xk to get xk 1 k 1 Evaluating the definite integral we obtain 10k 1 k 1 and so the normalizing constant is k 1 10k 1 R 10 ii E X k 1 10k 1 0 xk 1 dx 10 k 1 k 2 We set this equal to 8 and solve to get k 3 3 A Of course it depends on one s stomach for risk If we consider average risk then since expected profit is 14 0 2 1 0 8 2 0 we would go for it However if we consider downside risk then since the probability of losing million smackers is 0 8 which is really quite large so we may decide against this venture B Hopefully we have automatic response to this problem CLT Use a normal approximation the E profit on one venture is 2 and the standard deviation is easily worked out to be 6 lose 1 unit with probability 8 and gain 14 units with probability 2 Thus since n 25 using the central limit theorem with X N 50 302 we compute P X 0 P Z 50 30 0 0475 C i Our friend Bayes theorem once again we



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view STAT 101 Solutions Midterm Exam and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view STAT 101 Solutions Midterm Exam and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?