If an exponential random variable, X, has failure rate λ, what is E[X|X<λ]?
I'm not sure how to start here. I know that E[X] = 1 / λ for an exponential random variable. Is the probability that X < λ = 1-e^(-λ*λ)?
Can I use this identity E[X] = E[X|X < c]P{X < c} + E[X|X > c]P{X > c}?
Expectation[x \[Conditioned] x < \[Lambda], x \[Distributed] ExponentialDistribution[\[Lambda]]]– May 20 '15 at 21:00