I'm learning probability and trying to solve the following problem:
Determine $a,b$ so that probability density function will be: $\left\{\begin{matrix} x & x \in (0,1) \\ a+bx & x \in [1,2] \\ 0 & > else \end{matrix}\right. $.
However, I'm stuck at one step.
Here is my attempt so far:
$\int_{0}^{1} x dx = \frac{1}{2}$ --> not a probability density function
$\int_{1}^{2} a+bx dx = a+b\frac{3}{2}$
$a+b\frac{3}{2}=1$ --> stuck here. I'm not sure how to solve it and find values so that it would equal $1$.
Thanks