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S1 formula help!!

hey guys, i was preparing for the S1 exam on Wednesday when i came across these formulae in the textbook (page 175 S1 Edexcel red book):
E(X)= (n+1)/2
and
Var(X)=(n+1)(n-1)/12
I've never been taught those or seen them until today and i just wanted help as to how and when we use these.
please include an example if you can


thanks :smile:
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Avatar for izaman
izaman
This formula is to do with uniform distribution. For example a fair dice has 1, 2, 3, 4, 5, 6 on each of its faces and the probability of getting any of those numbers is always 1/6. If you used the original expected equation: E(X): sum(X*probability), it would be: (1 * 1/6) (2 * 1/6) (3 * 1/6) .... (6 * 1/6) = 3.5 Using this equation: E(X)= (n 1)/2, you simply count the number of X values, in this case it is 6, (n=6) and sub it into the formula (6 1)/2= 3.5 To be honest I would use E(X): sum(X*proability) instead of E(X)= (n 1)/2 because you get the same answer and the same applies to the variance.

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