How to find the variance of x from a given cumulative distribution function when the function contains no variable x?

Question

The way I see people going about it is first differentiating to get the p.d.f, then integrating over the given bounds to get the expected value, then using the formula for variance to find the variance from the expected value. But this c.d.f has no x variable that I can differentiate.

Answer 1

Using this we find $$E(X)=\int_0^5(1-F(x)) dx$$ and $$EX^2=2\int_0^5x(1-F(x)) dx$$ from which you can calculate the variance.