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January 31st, 2018, 04:12 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Random Sum of Random Variables
There are 400 individuals, each of whom has a 0.2 chance of incurring a claim. If the distribution of the individual claim amount, given that a claim has occurred, is uniform on the interval [0, 200]. Find the mean and variance of the total claim. I calculated the mean of total claim amount to be 8000 and the variance of the total claim amount to be 906,666.67, but I'm honestly not confident in this answer. I was struggling to justify it using conditional distributions and the iterated rule (which is what I assumed I was supposed to use), and instead just relied on intuition to arrive at those answers. Can somebody explain how to justify them, if they're correct? 

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random, sum, variables 
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