Probablity question (confused on the pdf)

[bennyska]

Homework Statement

$f(x)=\begin{cases}<br /> 7(4)^{-i} & x\in(\frac{1}{2^{i}},\frac{1}{2^{i-1}}],i=1,2,3,...\\<br /> 0 & 0\geq x,x>1<br /> \end{cases} (please excuse the poor latex)<br /> <h2>Homework Equations</h2><br /> <br /> <br /> <br /> <h2>The Attempt at a Solution</h2><br /> the problem I'm having is say x=3/4. then according to the pdf, shouldn't P(x)=7*(4^-1)=7/4>1. i mean, shouldn't it be bounded by 1? when i integrate this out, i get 1, like i should, so I'm not sure what mistake I'm making.$

 

[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

 

[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?

 

[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.

 

[bennyska]

oh, got it. duh. thank you.