- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 6. Expected Value (Mean), Variance, and Conditional Measures of Expected Value and Variance

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**CFA Practice Question**

Consider the following events:

S2: Fed increases interest rates in the first quarter of 2012

S3: Fed leaves interest rates unchanged in the first quarter of 2012

X: Earnings per share for a certain stock

P(S1)=0.3, P(S2)=0.35, P(S3)=0.35, E(X|S1)=3.35, E(X|S2)=3.67, E(X|S3)=3.52

B. $3.52

C. $3.57

S1: Fed decreases interest rates in the first quarter of 2012

S2: Fed increases interest rates in the first quarter of 2012

S3: Fed leaves interest rates unchanged in the first quarter of 2012

X: Earnings per share for a certain stock

We have the following information:

P(S1)=0.3, P(S2)=0.35, P(S3)=0.35, E(X|S1)=3.35, E(X|S2)=3.67, E(X|S3)=3.52

What is the unconditional expected value of the EPS?

A. $3.51

B. $3.52

C. $3.57

Correct Answer: B

The unconditional expected value is calculated as follows: E(X) = 3.35 x 0.3 + 3.67 x 0.35 + 3.52 x 0.35 = $3.5215.

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