- CFA Exams
- 2021 CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 4. The Discrete Uniform Distribution

###
**CFA Practice Question**

Suppose that the penalty for withdrawing funds early from a certain account follows a uniform distribution on the interval from (5%,12%). What is the probability that the penalty is between 6% and 9%?

B. 0.429

C. 0.882

A. 0.143

B. 0.429

C. 0.882

Correct Answer: B

The probability is P(6 < X < 9) = F(9) - F(6) = (9-5)/7 - (6-5)/7 = 0.429.

###
**User Contributed Comments**
18

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

mtcfa |
Huh??? Obviously I'm screwed on this section. |

dave79 |
Acutally, it's not that difficult: here is answer - 1) Find a and b in this problem 5=a and 12=b 2) now need to find probablity between 6% and 9% which lies betn distribution a and b 3) P(6<x<9) is equal to cummulative prob of 9 - cumm prob of 6 = F(x=9) - F(x=6) 4) F(x) = x-a/b-a 5) F(9) = 9-5/12-5 and F(6)= 6-5/12-5 6) = 4/7 - 1/7 = 3/7 =0.429 |

Bibhu |
Good explanation dave. |

bahodir |
Wait a minute... (5, 12) means 6, 7, 8, 9, 10, 11, doesn't it? The question should have written [5, 12] if they included 5 and 12 in the solution. |

bahodir |
Oh, I instead of 6, 7, 8, 9, 10, 11 I mean the range from 5 to 12 excluding these two numbers. |

Christian07 |
Why doing it that difficult? Total range => 12-5= 7, Selected Range => 9-6=3, therefore 3/7=0.429 |

bobert |
bahodir, you are correct that the numbers are not inclusive. BUT, because it is a uniform distribution, we are assuming it is continuous. Due to this fact, we know that the probability for a continuous random variable p(x) = 0 because there are an infinite number of possibilities. So just for the sake of correctness, the actual list of 6,7,8,9,10,11 is not important because each individual variable would then be p(6)=0, p(7)=0, and so on. What is important is the range of values between 5 and 12 and the formula to find the percentage of values within the parameters. This problem is asking for a CUMULATIVE probability within the parameter in reference to the range. |

rt2007 |
this is the formulae - (X2-X1)/(b-a) |

madhi |
Remember that we are trying here to compute an area of a rectangle. Hight of Rectangle = 1/(b-a) Required interval = 9%-6% = 3% Hence, the required probability equals the partial area = 3%/(b-a) = 3%/7% = 0.429 |

Meka76 |
Thanks guys, this really helped. |

CFAonTheBrain |
i'm not sure what im doing is right but i did this--- 5 - 12 = 7 and then 6 - 9 = 3 so 1/7 + 1/7 + 1/7 = .429 or .4285 |

jansen1979 |
Just draw a box with a minimum of 5 and a maximum of 12 and see which part you need to cover, will come clear this way. |

boddunah |
good question |

bp019j |
Thanks Christian07 |

cfaeater |
Great answer Christian07 - no nonsense explanation. |

sgossett86 |
Yeah, I did what Christian did intuitively. I'll memorize and apply the formula as needed, but I'm tired and this was an intuitive way. |

praj24 |
MAN LIKE CHRISTIAN07 |

cfastudypl |
Thanks Christian07 for the astute solution. |