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- 81

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## Homework Statement

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##-1\leq\alpha\leq 1##

##f(y_1,y_2)=[1-\alpha\{(1-2e^{-y_1})(1-2e^{-y_2})\}]e^{-y_1-y_2}, 0\leq y_1, 0\leq y_2##

and ##0## otherwise.

Find ##V(Y_1-Y_2)##. Within what limits would you expect ##Y_1-Y_2## to fall?

## Homework Equations

N/A

## The Attempt at a Solution

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I understand how to go about getting the variance of this distribution. That's not a problem. What I don't understand is finding the expected limits of ##Y_1-Y_2##. The book has the solution as ##\mu_{Y_1-Y_2} \pm 2*\sigma_{Y_1-Y_2}##. I can't find anything about this in my book with what's been covered thus far in this course or the last course. 2 standard deviations just seems rather arbitrary in this case. Is there a reasoning for 2 standard deviations? Possibly because the marginal distribution functions are exponential distributions, or because there's some convention to use 2 instead of say 1 or 3?

Note: This may actually be covered in the future weeks, as this book likes to use material from future sections in questions of previous sections. For example, in this question, the solutions in the back use the covariance to find the variance of ##Y_1-Y_2##, whereas covariance isn't introduced until the next section.