For the limiter shown below, find the expected value for Y = g(X)(adsbygoogle = window.adsbygoogle || []).push({});

attempt at solution:

E[Y] = ∫g(x)f(x)dx, where f(x) is the probability density function with respect to x

so...

E[Y] = E[Y_{1}] + E[Y_{2}] + E[Y_{3}]

E[Y_{1}] = ∫-af(x)dx where the limits of integration are from -∞ to -a

so E[Y_{1}] = -aF_{x}(-a), where F_{x}is the cumulative distribution function

E[Y_{2}] = ∫xf(x)dx where the limits of integration are -a to a

this is the part i'm having trouble with

E[Y_{3}] = ∫af(x)dx where limits of integration are a to ∞

so E[Y_{3}] = a(1-F_{x}(a))

i'm having trouble simplifying E[Y_{2}] into one expression because of the limits of integration. i know it would be just E[Y_{2}] if the limits were -∞ to ∞, but that is not the case here

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# Homework Help: Expected values of a limiter

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