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Probablity question (confused on the pdf)

  • Thread starter bennyska
  • Start date
  • #1
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Homework Statement

[itex]
$f(x)=\begin{cases}
7(4)^{-i} & x\in(\frac{1}{2^{i}},\frac{1}{2^{i-1}}],i=1,2,3,...\\
0 & 0\geq x,x>1
\end{cases}$ (please excuse the poor latex)

Homework Equations





The Attempt at a Solution


the problem i'm having is say x=3/4. then according to the pdf, shouldn't P(x)=7*(4^-1)=7/4>1. i mean, shouldn't it be bounded by 1? when i integrate this out, i get 1, like i should, so i'm not sure what mistake i'm making.
 

Answers and Replies

  • #2
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what is the actual question? Maybe I'm missing it, but it seems like you just posted an equation without any description of what you are trying to do
 
  • #3
jbunniii
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Why do you expect that a pdf must be bounded by 1? Consider a random variable that is uniformly distributed over the interval [0, 1/2]. Is that pdf bounded by 1?
 
  • #4
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well, the actual problem is show that this function is a pdf. so i need to show that it integrates to 1, which it does, but i believe i also need to show that it's bounded by 0 and 1 for all x in the domain, which is the problem i'm having a hard time with.
 
  • #5
112
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oh, got it. duh. thank you.
 

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