STA 135 Sample Exam I
Maxime Pouokam
Disclaimer : This is just a practice exam. If something is not cover here that does not mean it won’t be covered during the
actual exam.
True/False
For each of the following questions indicate true or false, then explain your answer. You may use examples to illustrate your
answer.
(I) Principal component analysis (PCA) can be used with variables of any mathematical types: quantitative, qualitative,
or a mixture of these types.
(II) If the covariance of two random variable X and Y equals 0, then they are independent.
(III) In multivariate analysis, we always need to scale the variable before performing PCA
(IV) The mahalanobis distance is always different to the traditional ||.||2 norm.
1
Full Detail
Work out the following problems. Show your work.
1. Let X and Y be jointly biviriate normal with V ar(X) = V ar(Y ). Show that the two random variables X + Y and
X Y are independent.
2. Let X1, X2 and X3 be independent and identically distributed 3× 1 random vecotrs with
μ = [3, 1, 1]T and
Σ =
3 1 1 1 1 0
1 0 2
