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April 13th, 2014, 10:41 AM   #1
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Is this pdf bounded?

The question asks to find the constant $\displaystyle c$ so that $\displaystyle f(x)$ is a pdf of a random variable $\displaystyle X$. Then asks is this pdf bounded?

I cannot find in my notes or text how to find if a pdf is bounded.

To solve for $\displaystyle c$
$\displaystyle f(x) =c/\sqrt{x}$ , $\displaystyle 0<x<1$
$\displaystyle \int_0^1 c x^{-1/2}=1$
$\displaystyle 2cx^{1/2}|_0^1$
$\displaystyle 2c\sqrt{1} -0=1$
$\displaystyle 2c=1$
$\displaystyle c=1/2$

So this pdf is bounded by zero, but no upper bound?

If there more work to this?

Thanks for any help!
WWRtelescoping is offline  
April 13th, 2014, 01:40 PM   #2
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You obviously saw that as x -> 0, f(x) -> ∞, which means it is not bounded.
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