Hi, I have a random variable V with probability density g(V) and a sigmoid, or logistic, function Y=S(V). I'd like to calculate a closed-form expression for the expected value of the sigmoid function transformation, i.e., a closed-form expression for E[Y]. My question is, for which standard probability density function can we write a closed-form expression for the expected value of the sigmoid function transformed r.v. Y? For example, uniform distribution is an obvious example of a density function that satisfies the requirement. I'd be very grateful for points anything whatsoever. Thank you!

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