# Thread: determine the constant in continuous random variable

1. ## determine the constant in continuous random variable

Can someone check thru my working? I cant find mymistake... The ans is b =4

2. ## Re: determine the constant in continuous random variable

you integrated wrong.

$f(x)=\begin{cases} \sqrt{\dfrac{x-1}{12}}&1\leq x\leq b\\ 0&\mbox{else} \end{cases}$

$\displaystyle{\int_1^b}f(x)~dx=1$

$\displaystyle{\int_1^b}\sqrt{\dfrac{x-1}{12}}~dx=1$

$\dfrac{(b-1)^{3/2}}{3\sqrt{3}}=1$

$b=4$