Homework Help: Probablity question (confused on the pdf)

1. Sep 3, 2012

bennyska

1. The problem statement, all variables and given/known data[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)
2. Relevant equations

3. 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.

2. Sep 3, 2012

smk037

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. Sep 3, 2012

jbunniii

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. Sep 3, 2012

bennyska

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. Sep 3, 2012

bennyska

oh, got it. duh. thank you.