- CFA Exams
- CFA Exam: Level I 2021
- 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**

The probability that the Fed increases interest rates is 35%. Given the increase in interest rates (event S), it is expected that the EPS distribution for a stock is as follows:

B. $1.125; 0.0625

C. $1.2; 0.0475

What are the expected value and variance?

A. $1.125; 0.0076

B. $1.125; 0.0625

C. $1.2; 0.0475

Correct Answer: C

The variance is calculated as follows: V(X|S) = (0.75 - 1.2)

The expected value is calculated as follows: E(X|S) = 0.75 x 0.05 + 1 x 0.35 + 1.25 x 0.35 + 1.5 x 0.25 = $1.2

The variance is calculated as follows: V(X|S) = (0.75 - 1.2)

^{2}x 0.05 + (1 - 1.2)^{2}x 0.35 + (1.25 - 1.2)^{2}x 0.35 + (1.5 - 1.2)^{2}x 0.25 = 0.0475###
**User Contributed Comments**
14

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

noonah |
Having worked out the conditional expectation as 1.2, the variance could only be positive, and hence answer is C without having to perform the calculation |

tssverma |
good guess noonah |

RichWang |
BA II Plus can get SIGMA (XY) = 1.2, but can BA II Plus get variance? How about BA II Plus Professional? |

surob |
RichWang, can you please explain how to use SIGMA (XY)on BA II? |

tagr |
2ND-STAT Fill in values of table above for X and Y 2ND-QUIT 2ND-STAT Push up arrow gives SigmaXY = 1.2* |

bobert |
I am still lost on how to do it on the BAII+. |

Frehner |
On BA II Plus Professional 2nd Data 2nd Clr Work Fill in X for column one and Y for column two 2nd Stat Up Arrow |

bdoggprod |
Thanks for the info on the BAII + |

strike |
how about for hp 12c? |

raymondg |
Thanks for the calculator tip. Could you also calculate the varience? |

jpducros |
For HP 12c, 0.75 enter 0.05 Sigma+ 1 enter 0.35 Sigma+ 1.25 enter 0.35 Sigma+ 1.50 enter 0.25 Sigma+ g xbarw (in other words, number 6) result is 1.2 is the weighted mean. |

NikolaZ |
@ Frehner: I get 1.125 as the mean using your method, any idea why? |

Shaan23 |
If you want to push less buttons and understand whats going on ---- DONT USE CALCULATOR HERE Only use calculator on time value money question |

Huricane74 |
I recommend that people do it both ways. First to understand what is going on so that you can do more complex problems later on. However, on the exam, you are pressed for time, so you have to learn how to do it on a calculator. I prefer using the BAII plus. |