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I'm trying to understand why when you have a muon decay event, the energy of the electron peaks near the maximum kinematically allowed value. Is there an intuitive explanation for why this is the case or is it one of those things where the explanation is that it's just how the math works out?

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Step one: analyze the decay kinematics in the muon's rest frame (controlled by angular momentum considerations). Step two: boost to the lab frame. –  dmckee Dec 5 '12 at 17:35
    
I did, the entire range of energies is allowed, and you don't get a probability density this way. Brute force calculation of the differential cross section and taking the derivative of E gives the desired result. I'm just looking for an intuitive understanding. –  user788171 Dec 6 '12 at 0:31
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