### CFA Practice Question

There are 410 practice questions for this study session.

### CFA Practice Question

The joint probability function for X and Y is as follows: What is the covariance between X and Y?

A. -1.1015
B. -0.0075
C. 0.3065

Use the shortcut formula: Cov(X, Y) = E(XY) - E(X)E(Y).
First compute E(XY) = 1.1 x 0.5 x 0.15 + 1.4 x 0.5 x 0.35 + 1.1 x 0.7 x 0.4 + 1.4 x 0.7 x 0.1 = 0.7335.
Then compute the expected value for each variable:
E(X) = 1.1 x (0.15 + 0.4) + 1.4 x (0.35 + 0.1) = 1.235
E(Y) = 0.5 x (0.15 + 0.35) + 0.7 x (0.4 + 0.1) = 0.6
The covariance is then:
Cov(X,Y) = 0.7335 - 1.235 x 0.6 = -0.0075

User Comment
spartan how do you do this problem
sunilcfa Exactly the way shown in the answer
3CCI how do u arrive the shortcut formula? it's not anywhere in the notes provided. is it possible to do it any other way (with better clarity?)
Rotigga Without the shortcut formula:
Cov=E[(X-E(X))*(Y-E(Y))]
E(X)=1.1*(0.55) + 1.4*(0.45) = 1.235
E(Y)=0.5*(0.5) + 0.7(*0.5) = 0.6
Cov=(1.1-1.235)(0.5-0.6)*0.15 + (1.4-1.235)(0.5-0.6)*0.35 + (1.1-1.235)(0.7-0.6)*0.4 + (1.4-1.235)(0.7-0.6)*0.1 = -0.0075 (B is correct)
soarer1 Is there a method using BAII?
wacarinci little advice for everyone looking for shortcuts with calculator...start learning and workign these problems out to better understand what you are doing. the real exam is much more theory, applying theory and far less calculations. you will hardly use your calc on exam.