- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 6. Expected Value, Variance, and Standard Deviation of a Random Variable

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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)=0.65, P(S2)=0.10, P(S3)=0.25, E(X|S1)=1.75, E(X|S2)=1.50, E(X|S3)=1.67

B. $1.69

C. $1.705

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)=0.65, P(S2)=0.10, P(S3)=0.25, E(X|S1)=1.75, E(X|S2)=1.50, E(X|S3)=1.67

What is the unconditional expected value of the EPS?

A. $1.64

B. $1.69

C. $1.705

Correct Answer: C

The unconditional expected value is calculated as follows: E(X) = 1.75(0.65) + 1.50(0.10) + 1.67(0.25) = $1.705.

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**User Contributed Comments**
6

User |
Comment |
---|---|

mrushdi |
good question |

harpalani |
Guys, I'm clueless on this. I thought the given answer is "conditional" expected value and NOT "unconditional" expected value. Can someone pls.share thoughts on this? |

joywind |
@harpalani, the answer is "unconditional" expected value, a sum of those "conditional" expected values under different conditions |

idzani |
Technically by summing the individual E(x)s you are getting the expected value for all circumstances i.e. unconditional |

choas69 |
good explanation idzani |

Huricane74 |
The easiest and fastest way to do this is on the calculator by entering value for X and Y using the [DATA] and [STAT] function. Set up a table to make sure you are entering the values correctly. Toggle down until you get to the function: ΣXY = |