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#1




TIA Exam 2 #5 Variance with a deductible
I don't understand why the solution to this problem used a method other than using the formulas given for the exponential but no mention is made why they were not.
Given an exponential with a deductible and we are asked to find the variance of the payment, why can't the formula (Ex^2  E[x^d]^2)  (same for Ex)^2 be used? The solution to this problem uses a form of the double expectation/variance formula for the variance. Well, that formula never made any intuitive sense to me so I am wondering why that was chosen for the solution to this problem rather than what would seem to be the simpler approach using the formulas given and then just plug in values. Anyone know? If not, does anyone understand the method that was used in the solution? Thanks. 
#2




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Calculate the variance as the mean of the variances plus the variance of the means (which can be done using the bernoulli shortcut). The formula simplifies and might be worth memorizing. 
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