Question 5081
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Help--how do i figure this one out? Driving me crazy !!!
Twenty bearded men gather. Ten have eight-inch beards, six have ten-inch beards, and four have twelve-inch beards. 
What is the expected length of a randomly selected man from this group?
Tried 10/20 x 6/20 x 4/20 =12inches, that doesn't seem right. Please help!
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The problem asks about the mathematical expectation.


According to the definition of this quantity, we should calculate


    {{{8*(10/20) + 10*(6/20) + 12*(4/20)}}} = {{{(1/20)*(80 + 60 + 48)}}} = {{{188/20}}} = 9.4 inches.


<U>ANSWER</U>.  The expected length is 9.4 inches.
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Solved.