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April 13th, 2014, 11:41 AM  #1 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  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 $\displaystyle c$ $\displaystyle f(x) =c/\sqrt{x}$ , $\displaystyle 0<x<1$ so $\displaystyle \int_0^1 c x^{1/2}=1$ $\displaystyle 2cx^{1/2}_0^1$ $\displaystyle 2c\sqrt{1} 0=1$ $\displaystyle 2c=1$ $\displaystyle c=1/2$ So this pdf is bounded by zero, but no upper bound? If there more work to this? Thanks for any help! 
April 13th, 2014, 02:40 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625 
You obviously saw that as x > 0, f(x) > ∞, which means it is not bounded.


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