- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 6. The Normal Distribution

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**CFA Practice Question**

For x, a normal random variable, which of the following is (are) false?

II. The parameters are the mean and standard deviation.

III. The graph is a bell-shaped curve.

IV. The probability x is equal to a particular value (say, 55) is zero.

I. The parameters are N and p.

II. The parameters are the mean and standard deviation.

III. The graph is a bell-shaped curve.

IV. The probability x is equal to a particular value (say, 55) is zero.

Correct Answer: I only

N and p are parameters for a binomial random variable.

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**User Contributed Comments**
7

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

standaert |
why is anser IV correct? |

kevin |
IV is correct as you can only calculate the probability of x when it falls in a range, such as 56 > x > 54. The probability of x equaling to one exact value is definitely 0. |

surob |
It is because it is continuous distribution |

bobert |
Because in a continuous distribution there are unlimited potential outcomes between the ranges, say -infinity to +infinity. so if you have a value of X = 55 like the example, it would be X/infinity or 55/infinity. This is mathematically impossible though because infinity is not a real number. It would be successively smaller and smaller, but how do you calculate an always decreasing number? Simply put, you cant. 0 would be the limit to which it can go because as infinity increases in the denominator, the probability would get smaller and smaller. As I had said however, infinity is a concept, a word, therefore do not think that x/infinity = 0. Sorry for the long winded explanation, just hope to make it clear. |

Yurik74 |
bobert - mathematician? |

Dsatti |
But its not EQUAL to zero, it tends to zeros as n tends to infinity does it not? So mathematically you can't say it equals zero?! |

johntan1979 |
Prove it, Mr Wiseguy. |