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A quiz on the concepts of covariance and correlation for the ie230 exam. It includes questions on the definition of covariance and correlation, the relationship between means and covariance, and the properties of correlations. It also assumes a multivariate normal distribution for a set of variables and asks about the parameters of the distribution. This quiz is intended for university students taking the ie230 exam.

Typology: Quizzes

Pre 2010

1 / 1

Download Quiz on Covariance and Correlation for IE230 Exam - Prof. Bruce W. Schmeiser and more Quizzes Probability and Statistics in PDF only on Docsity! Quiz 10. November 15, 2006 Family Name, Initials, Seat #: < at top, on back > Closed book and notes. No calculator. Recall: Cov(X , Y ) = σX σY Corr(X , Y ). Recall: If Y = a 1X 1 + a 2X 2 + . . . + ak Xk , then E(Y ) = a 1E(X 1) + a 2E(X 2) + . . . + ak E(Xk ) and V(Y ) = i =1 Σ k j =1 Σ k ai aj Cov(Xi , X j ) . For Questions 1–10, consider this context. The experiment is to choose a student from this class. Let Y denote this semester’s over-all numerical score. Let Xi denote the numerical score on this semester’s IE230 Exam i , for i = 1, 2, 3, 4. Let Xi +4 denote the score for Quiz i for i = 1, 2,...,11. (Assume that all covariances are positive.) 1. In each replication of the experiment, how many students are chosen? one ← 2. In words or numerical value, what is the value of a 1? The weight for Exam 1, which is a 1 = 0.2 ← 3. T ← F Y is a random variable. 4. T F ← "X 1 > X 2" is a random variable. 5. T ← F All correlations are positive. 6. T← F All correlations are no larger than one. 7. T ← F Corr(X 1, X 2) = Corr(X 2, X 1). 10. T F ← If X 1 < E(X 1), then Cov(X 1, Y ) < 0. For Questions 9–10, now also assume that (X 1, X 2, . . . , X 15, Y ) is a 16-dimensional normal random vector. Then any pair of vector components is a bivariate normal random vector. 9. What are the parameters of the distribution of (X 1, X 2)? µX 1 , µX 2, σX 1, σX 2, ρX 1,X 2 ← 10. State the (approximate) values of the parameters from Question 9. µX 1 = 66, µX 2 = 75, σX 1 = 12, σX 2 = 12, ρX 1,X 2 = 0.4 ← IE 230. – Page 1 of 1 – Schmeiser