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Two fair and independent dice (each with six faces) are thrown. Let $X_1$ be the score on the first die and $X_2$ the score on the second. Let $X = X_1 + X_2$ , $Y = X_1 X_2$ and $Z = \min(X_1; X_2)$.

How would you calculate the variance of $Z$?

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    hint: $X_1$ and $X_2$ are discrete uniform random variables2012-10-31
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    so would i just take the expected value of the two and sum them?2012-10-31
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    Nope. Just calculate the distribution for $Z$ and then it's variance.2012-10-31
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    I'm not too sure how to get that... I'm very confused when it involves the minimum and maximum2012-10-31
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    How would I calculate the distribution for Z?2012-10-31
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    look [here](http://stats.stackexchange.com/questions/220/how-is-the-minimum-of-a-set-of-random-variables-distributed)2012-10-31
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    What I get from this is that I would find the cdf, differentiate to get the pdf and find variance from there?2012-11-01
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    Also in that link, it says that to calculate the cdf, we would evaluate the function at the certain value that we want to be smaller than.. In this case, would I use the case where x1x22012-11-01
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    I was asked to find the variance for the X and Y but I already calculated those2012-11-01
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    It would have been better not to include information that relates to things you didn't need a response on; it worried me at first as well.2012-11-01

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