How to Convert Between CDF and PDF Functions in Mathematical Equations?

[scot72001]

cdf to pdf and vise versa
hi
i'm looking for help when going from a cdf function:
F(x) = { 1- e^-αx^β x ≥ 0, α>0, β>0
{ 0 x < 0

to getting the corresponding pdf

also i am looking to do the opposite(pdf to cdf)
for:
f(x) = { (1 + α)/2 for -1 ≤ x ≤ 1, -1 ≤ α ≤ 1
{ 0 otherwise

i'm unsure as to how to integrate and differentiate these parts.
can you help please

thanks
michael

 

[whs]

You don't need to post the same question in multiple places.

 

[scot72001]

sorry i just noticed it said put homework in the homework section after i had posted it in the first location

 

[whs]

As for differentiating, you need to use the chain rule. Integrating that function should be simple since (1 + a)/2 is a constant with respect to X.

 

[scot72001]

so would the following look ok for the first part?
f(x) = {e^-αx^β } {αβ [x^(β-1) } x ≥ 0, α>0, β>0

and for the second part it should look like
f(x) = { (1 + αx)/2 for -1 ≤ x ≤ 1, -1 ≤ α ≤ 1 to start off. apologies for missing the x as it is crucial. do you think i can still use 1+α as a constant
then the answer would look like
((1 +α)x^2)/4