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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: onlyfknhuman on November 07, 2008, 08:17:15 am

Title: How to prove if its a probability Density function
Post by: onlyfknhuman on November 07, 2008, 08:17:15 am: Area = 1

and its continuous right?
Title: Re: How to prove if its a probability Density function
Post by: Mao on November 07, 2008, 12:26:51 pm: yep
Title: Re: How to prove if its a probability Density function
Post by: shinny on November 07, 2008, 12:35:59 pm: In methods, do we have to prove:
$f(x) \ge 0, x \epsilon R$
$Area=1$
And continuous?

Or just the area? Quite tedious to prove the other two at times <_<
Title: Re: How to prove if its a probability Density function
Post by: /0 on November 07, 2008, 06:31:23 pm: It does not have to be continuous
Title: Re: How to prove if its a probability Density function
Post by: onlyfknhuman on November 07, 2008, 06:32:08 pm: how come?
Title: Re: How to prove if its a probability Density function
Post by: shinny on November 07, 2008, 06:40:20 pm: Yeh I was thinking about that after...doesn't need to be continuous does it? Theres plenty of distributions which just cut off. But they have to at least be defined over R yes? (i.e. no 'gaps' in the domain. Everything must be assigned a value, even if it means y=0)
Title: Re: How to prove if its a probability Density function
Post by: Mao on November 07, 2008, 06:43:35 pm: Quote from: DivideBy0 on November 07, 2008, 06:31:23 pm
It does not have to be continuous

I can kind of see your point... however, it has to have a definite area bound by two ends though.

for example, you cannot define a continuous random probability function for $p(x)=x^{-1},\; x\in(0,k]$ (unless, of course, k is infinitesimal.... but lets not go into that)
Title: Re: How to prove if its a probability Density function
Post by: onlyfknhuman on November 07, 2008, 06:44:55 pm: ah fudge i see.
Title: Re: How to prove if its a probability Density function
Post by: Pandemonium on November 07, 2008, 06:57:52 pm: Quote from: Mao on November 07, 2008, 06:43:35 pm
Quote from: DivideBy0 on November 07, 2008, 06:31:23 pm
It does not have to be continuous

I can kind of see your point... however, it has to have a definite area bound by two ends though.
PDFs must have definite end points. yo.
for example, you cannot define a continuous random probability function for $p(x)=x^{-1},\; x\in(0,k]$ (unless, of course, k is infinitesimal.... but lets not go into that)