Can you help me with the following question?
I am given that X is Unif([-5,5]) and I am asked to calculate P(x belongs [2,7]). Now, I know how to calculate the probability that x belongs [2,5], and I also know for any x > 5, the probability is 1. But now, I do not know how to continue from this point and how to combine those two. Thank's in advance.
The sets $[2,5]$ and $(5,7]$ are disjoint, so the probability of $X$ belonging in their union is the sum of their respective probabilities. $$P_X(X \in [2,7])=P_X(X\in [2,5]\cup(5,7])=P_X(X \in [2,5])+\underbrace{P_X(X\in(5,7])}_{=0}$$ So you just have to compute $$P_X(X \in [2,5])=\frac{1}{10}\int_2^5dx=\frac{3}{10}$$