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CIE AS level Further Math - Stats
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oprahwindfuryy
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hi guys!! 
does anyone know if the mean of a probability density function can be greater than 1? thank you!!
does anyone know if the mean of a probability density function can be greater than 1? thank you!!
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ghostwalker
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(Original post by oprahwindfuryy)
hi guys!! does anyone know if the mean of a probability density function can be greater than 1? thank you!!
hi guys!!
does anyone know if the mean of a probability density function can be greater than 1? thank you!!
I take your question to mean you're refering to the mean of the pdf itself, rather than the mean of the r.v with that pdf.
If you restrict yourself to the values where the pdf is non-zero, then yes, it can be greater than one.
E.g. Consider the pdf of a uniform continuous distribution on the interval [0,0.1], then it's pdf is f(x)=10 on the interval [0,0.1], and zero elsewhere. The mean, restricted to the non-zero interval, is 10.
Note: Strictly speaking a pdf is defined from minus infinity to infinity, and it's mean value, over the whole of the reals, will always be zero.
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oprahwindfuryy
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(Original post by ghostwalker)
I take your question to mean you're refering to the mean of the pdf itself, rather than the mean of the r.v with that pdf.
If you restrict yourself to the values where the pdf is non-zero, then yes, it can be greater than one.
E.g. Consider the pdf of a uniform continuous distribution on the interval [0,0.1], then it's pdf is f(x)=10 on the interval [0,0.1], and zero elsewhere. The mean, restricted to the non-zero interval, is 10.
Note: Strictly speaking a pdf is defined from minus infinity to infinity, and it's mean value, over the whole of the reals, will always be zero.
I take your question to mean you're refering to the mean of the pdf itself, rather than the mean of the r.v with that pdf.
If you restrict yourself to the values where the pdf is non-zero, then yes, it can be greater than one.
E.g. Consider the pdf of a uniform continuous distribution on the interval [0,0.1], then it's pdf is f(x)=10 on the interval [0,0.1], and zero elsewhere. The mean, restricted to the non-zero interval, is 10.
Note: Strictly speaking a pdf is defined from minus infinity to infinity, and it's mean value, over the whole of the reals, will always be zero.
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