Monday, June 6, 2016

probability - Show $mathbb{E}(X) = int_0^{infty} (1-F_X(x)) , dx$ for a continuous random variable $X geq 0$

If $X$ is a continuous random variable with density $f_X$ and taking non-negative values only, how do I show that $$\mathbb{E}(X)=\int_0^{\infty}[1-F_X(x)]dx$$ whenever this integral exists?

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analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...