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July 27th, 2018, 12:16 PM   #1
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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
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July 27th, 2018, 02:05 PM   #2
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$\displaystyle \int_{0}^{\infty}\!\! f(x)dx = \int_{0}^1\! f(x)dx + \int_{1}^{\infty}\!\! f(x)dx$ and that last integral is zero.
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