Hello friends could help me with this problem since reading a bit of statistics appeared but I can not solve it. Your help would help me out of doubts.
Find the distribution function $F$ of the random variable $X$ if its density is $$ f (x) = \begin{cases} x + 1, & -1 \le x \le 0\\ 1 - x, & 0 \le x \le 1 \end{cases} $$ Also, find the mean and variance of the continuous random variable $X$.
Hint:
$$F_X(x)=\int_{-\infty}^x f_X(t)\; dt$$ You will have to compute this piecewise since $f_X$ is given piecewise.
Do you know the definition of the mean and variance?