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July 27th, 2018, 01:16 PM  #1 
Newbie Joined: Jan 2018 From: brazil Posts: 4 Thanks: 0  Calculating probabilities
I have a random variable that is defined by this probability function: $\displaystyle f(x) = kx^³$ $\displaystyle 0<x<1$ $\displaystyle f(x) = 0,$ for x outside the above interval It then asks for the probability, so that the variable has a value between 1/4 and 3/4. First I tried to calculate the $\displaystyle \int_{0}^{\infty} f(x)dx = 1 $ to determine the value of k. Then I obtain: $\displaystyle k * \left.\frac{x^4}{4}\right_0^\infty = 1$ This way I will end with: $\displaystyle \infty  0 = 1 $. So what am I doing wrong? Thanks for the time 
July 27th, 2018, 03:05 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,951 Thanks: 1842 
$\displaystyle \int_{0}^{\infty}\!\! f(x)dx = \int_{0}^1\! f(x)dx + \int_{1}^{\infty}\!\! f(x)dx$ and that last integral is zero.


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