- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 4. The Discrete Uniform Distribution

###
**CFA Practice Question**

The St. Helens Insurance Company can maintain its risk-based capital ratio, or improve upon it, if its net income is at least $125 million. If earnings can fall anywhere from -$50 million to $500 million with equal probability, what is the likelihood the company can improve its risk-based capital ratio?

A. 68.2%

B. 67.3%

C. 69.1%

**Explanation:**This is a continuous uniform distribution, where b = $500 million and a = -$50 million. F(x) = (x - a)/ (b - a) for a < x < b; F(x) = 0 for x <= a, and F(x) = 1 for x >= b. We are solving for 1 - F(125) = 1 - (125 - (-50))/(500 - (-50)) = 1 - 175/550 = 68.2%.

###
**User Contributed Comments**
4

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

tanyak |
Can someone explain this question? |

micheleus |
improve their risk-based capital means: from 126 to 500 ---> P = 550-125 = 375. range of risk-base captital ratio: -50 to 500 ---> total P= 550. P(improve)=375/550=68.18% |

capitalpirate |
thx micheleus.. clear and concise |

aakash1108 |
good question! reality check! |