1. ## probability distribution function

Calculate the probability distribution function for the following density function

but I did not realize how the constant factor = -1 has been calculated please help thanks

2. ## Re: probability distribution function

Originally Posted by mhhjti
Calculate the probability distribution function for the following density function

but I did not realize how the constant factor = -1 has been calculated please help thanks
I do not know exactly what you are asking for!
But do you realize that this must be true:
$\displaystyle \lim _{t \to 1^ - } F_X (t) = \lim _{t \to 1^ + } F_X (t)$

3. ## Re: probability distribution function

Originally Posted by mhhjti
Calculate the probability distribution function for the following density function

but I did not realize how the constant factor = -1 has been calculated please help thanks
I think you have wrote the starting line of your question incorrectly.. You already have the probability distribution function $\displaystyle f_X(x)$ and you are supposed to find the cumulative distribution function $\displaystyle F_X(x)$. Looks like you have written the opposite.

please look at how you can find the cumulative distribution function of a random variable . You have to integrate the pdf over ...... region

4. ## Re: probability distribution function

Originally Posted by harish21
I think you have wrote the starting line of your question incorrectly.. You already have the probability distribution function $\displaystyle f_X(x)$ and you are supposed to find the cumulative distribution function $\displaystyle F_X(x)$. Looks like you have written the opposite.
Actually the OP is correct. S/he just used the wrong word.
You are correct most do use pdf & CDF. But the method is correct.
S/he simply was confused about the accumulation from the first integral.