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June 6th, 2017, 04:11 PM   #1
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A die is loaded so that the probability of a face coming up is proportional to the nu

A die is loaded so that the probability of a face coming up is proportional to the number on that face. The die is rolled with outcome X. Find V (X) and D(X).
How would you find the Expected value E(x) and the variance V(x) for this problem?

For this problem, I knew that the probability for each outcome would be x/21. And I knew that X=1,2,3,4,5,6 so I took the expected value of 1× (1/21)+2× (2/21)+3×(3/21)+4×(4/21)+5×(5/21)+6×(6/21) and got 3, then I tried to find the variance by using V(x)=E(x^2)-(E(x))^2=12, but the answer was 3/4 for V(x).
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June 6th, 2017, 05:26 PM   #2
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Redo your arithmetic. Mean=91/21.
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June 6th, 2017, 05:49 PM   #3
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So is the procedure right?
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June 6th, 2017, 09:19 PM   #4
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Quote:
Originally Posted by poopeyey2 View Post
So is the procedure right?
$E[X] = \sum X p[X] = \sum \limits_{k=1}^6 \dfrac{k}{21}k$

$V[X] = E[X^2] - (E[X])^2 = \left(\sum \limits_{k=1}^6 \dfrac{k}{21}k^2\right) - (E[X])^2$
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