CFA Practice Question

CFA Practice Question

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

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).

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?
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