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#1




SOA # 147 E(X)= lambda? 1/lambda^1?
I looked up SOA solution and the Ex=lambda and Variance=lambda^2.
But Wikipedia and the book I bought: Probability for Dummies says Ex of the exponential distribution is lambda^1 and variance is 1/lambda^2. Can someone please tell me which one is right? I don't understand why the one says one thing and the other says the other. And I searched the forum and everyone is assigning random variable Y to the amount of claim after deductible. Is additional random variable needed in this question? I just started studying probability and I am not that far in understanding the entire probability theory yet. I am sorry about asking what seems to be a basic for some people. Thank you. Last edited by yhanc17; 08132018 at 09:24 AM.. 
#2




There are two common ways of parameterizing an exponential:
(1) If you write the pdf in the form then the expected value is . (2) If you write the pdf in the form then the expected value is just the parameter which is nice. It might seem a bit weird to use the first form and call the parameter of the exponential , but the reason is because of its connection to the Poisson with parameter in the context of a poisson process. To be precise: If the number of events in any time interval of length is Poisson with parameter and the number of events in disjoint intervals are independent, then the time between any two events is exponential with parameter as in (1) above. That's the connection. EDIT: You have misquoted wiki above. The variance of an exponential is always the square of its mean. In (1) they are and . In (2) they are and . I hope that helps. Last edited by Michael Mastroianni; 08122018 at 06:37 PM.. 
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