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You roll a standard 6-sided die. Find the expected value for each experiment.

(a) You earn 6 points for each dot on the side that lands up. 
_____ points 

(b) You earn 6 points if it lands on a composite number and lose 6 points if it does not land on a composite number. 
_____ points

 Sep 28, 2018

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a) \(E[X]=\sum \limits_{k=1}^6~\dfrac 1 6 (6k) = \dfrac{6\cdot 7}{2} = 21\)

 

b) \(E[X] = \dfrac 1 6(6 + 6 + 6 - 6 + 6 - 6) = 2\) (1,2,3,5 are !composite, 4 and 6 are composite)

 Sep 28, 2018

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