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Finding the cdf of a continuous variate watch

1. Let be a continuous random variate with pdf for and otherwise.

I need to find the cdf of .

I know that, in general,

But in this case, I'm not sure where to integrate between. I tried integrating between [0, x] and [x, 1] but that just gives 1. So any help would be appreciated.
2. (Original post by MR1999)
Let be a continuous random variate with pdf for and otherwise.

I need to find the cdf of .

I know that, in general,

But in this case, I'm not sure where to integrate between. I tried integrating between [0, x] and [x, 1] but that just gives 1. So any help would be appreciated.
Your general formula is correct, and in this case the lower bound will be 0, since f(x) is 0 below x=0.

I can't make sense of "I tried integrating between [0, x] and [x, 1]" - sounds like you're integrating between two intervals???

Your limits should just be 0 and x, and you end up a function of x.

I'm going to have to keep my responses brief, as I keep getting "Service not available", and even when it is, the screen and cursor are jumping around all over as it's so f**king slow!
3. (Original post by MR1999)
Let be a continuous random variate with pdf for and otherwise.

I need to find the cdf of .

I know that, in general,

But in this case, I'm not sure where to integrate between. I tried integrating between [0, x] and [x, 1] but that just gives 1. So any help would be appreciated.
Just evaluate , which is valid for

EDIT: Obviously integrating over [0,x] then adding on the integral over [x,1] will give you 1. This is the same as integrating your density function over in this case, and we know this must be 1 since you're summing all the probabilities!

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