1. ## CDF to PDF

2. Originally Posted by NaeL
For CDF $\displaystyle F(x)$ and PDF $\displaystyle f(x),$ we have the relation...
$\displaystyle \frac{d}{dx}F(x) = f(x)$
Also, you know $\displaystyle \int_a^b f(x) = 1$ where $\displaystyle x$ is defined on $\displaystyle a<x<b...$ You can use this fact to find $\displaystyle K.$
For the last part note that $\displaystyle F(x) = P(X\leq x)$ and $\displaystyle F(x)$ is given. Also, $\displaystyle P(a\leq x \leq b) = \int_a^b f(x)dx.$