# Probablity question (confused on the pdf)

## 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)

## 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

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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

jbunniii
Homework Helper
Gold Member
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?

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.

oh, got it. duh. thank you.