Jake has $100 dollars in his wallet. He spends $15 at Tastee Sub and $10 at Wawa. As he is walking home, Jake finds a $20 bill o
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You can compute both the mean and second moment directly using the density function; in this case, it's
Then the mean (first moment) is
and the second moment is
The second moment is useful in finding the variance, which is given by
You get the standard deviation by taking the square root of the variance, and so