$X$ is a random variable with distribution function given by:
$$F_X(x) = \begin{cases} 0 & :\text{if }x < 0 \\[1ex] 1/4 & :\text{if }0 \le x < 1 \\[1ex] 2/5 & :\text{if }1 \le x < 2 \\[1ex] \dfrac{2x - 3}{2} & :\text{if }2 \le x < 2.5 \\[1ex] 1 & :\text{if }x > 2.5 \end{cases}$$
I need to find $E(X)$ from this function but I'm struggling to do that. I'm new to stats and I'm trying to solve this problem. Can, please, someone help me?
The answer for this is $59/40$
You have three step discontinuities (indicating point masses) at $(0,\tfrac 1 4), (1, \tfrac 25) , (2, \tfrac 12)$
You have a uniform distribution from $2, .. ,2.5$
So $$\mathsf E(X) = 0\cdot(\tfrac 14) + 1\cdot(\tfrac 2 5-\tfrac 1 4)+2\cdot(\tfrac 1 2-\tfrac 2 5) + \int_{2}^{2.5} x \dfrac{\operatorname d \frac{2x-3}{2}}{\operatorname d x}\operatorname d x$$