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**CFA Practice Question**

Which of the following is (are) true about a normal distribution?

II. It has a positive third moment.

III. It is symmetrical about zero.

I. It has only one mode.

II. It has a positive third moment.

III. It is symmetrical about zero.

A. I & III

B. I only

C. I, II and III

**Explanation:**A normal distribution is symmetrical about the mean, which can be non-zero. It has a zero third moment (zero skewness).

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**User Contributed Comments**
13

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

bonzino |
0 can be positiv and negativ isn't? |

kuan |
vs standard normal distribution.. question just playing with words! |

eddeb |
What's the third moment? Thanks |

armanaziz |
I remember third moment is [Sum(Xi-Xbar)^3]/n Am I correct? |

Carol1 |
No should be Sum(Xi-Xbar)^3/n*Var(x)^3 |

jckasn |
Can a normal distribution not have more than one mode? what if it has more than one observation appearing the same number of times?? |

dimanyc |
jckasn, before i answer your question, please look up the definion of the "mode" :) |

Dinosaur |
third moment is the skewness? |

todolist |
by the same token i guess 4th moment is kurtosis? |

MrsP |
See Wikipedia "Significance of the moments" 1st moment --> The first moment about zero, if it exists, is the expectation of X, i.e. the mean of the probability distribution of X, designated μ. In higher orders, the central moments are more interesting than the moments about zero. 2nd moment --> Variance 3rd moment --> Skewness 4th moment --> Kurtosis |

Andrewua |
good Q! Here it goes about normal, but not std normal, so 3 doesn't fit! |

mattg |
crud I went for the "symmetrical around 0" one - gotta read more carefully! |

MaresaJaden |
Mode = Value that occurs most frequently... Everything I read says there can be more than one mode in a data set. How does it being a 'normal' distribution change this? Can anyone direct me to the source of this data? |