Find distribution function given p.d.f

mutzy188
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Homework Statement



The probability density function of X is f(x) = 2x, 0 < x < 1
Find the distribution function of X.

The Attempt at a Solution



I just don't know what to do here. The book does something with Y and the change of variables and I don't understand why they were doing that. I had origionally thought that to do this problem I would just have to integrate the function??
 
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Change of variables?

What is a distribution function? Ask yourself that question first. You will find that a distribution function is...

F(x) = P(X<=x)=Integral(x,-infinity)f(t)dt

That's it. You are integrating the function. Change of variables? No. I'll let you work from here.

Note: I'm like you. If I don't know what I'm doing, I'm just like... change of variables? Jacobian? Screw this!
 
k Thanks
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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