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uniform contiuous probability
Message posted by Tanya G. on November 2, 1999 at 12:00 AM (ET)
Hello,
I am currently enrolled in a college statistics course, where my instructor has asked her students to find out what the '12' means in the formula for the variance of the uniform contiuous probability:
Var(x)= ((b-a)^2)/12
What does the 12 represent or where does it come from? If anyone knows the answer, I would greatly appreciate you help.
Thank you, TG
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: uniform contiuous probability
Message posted by JG on November 3, 1999 at 12:00 AM (ET)
The 12 comes from calculationg the variance with calculus. We end up with 2*(1/3)*(.5)**2 which equals 1/12 .
Re: uniform contiuous probability
Message posted by Jack Tosmky on November 3, 1999 at 12:00 AM (ET)
The following is a formal derivation. If X is uniform between a and b, thenX = a+(b-a)*U, where U is uniform between 0 and 1.
Var(X) = [(b-a)^2]*Var(U)
Var(U) = E(U^2)-[E(U)]^2
E(U^2) = 1/3
E(U) = 1/2
Var(U) = 1/3 - 1/4 = 1/12
Var(X) = [(b-a)^2]/12
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