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Verifying statistical identities.?
Verify the following identities
sum of (-1)^k * (n choose k) as k goes from 0 to n is equal to 0
sum of k * (n choose k) as k goes from 1 to n is equal to n * 2^(n-1)
sum of (-1)^k * k * (n choose k) as k goes from 1 to n is equal to 0
Assume that n is greater than or equal to 2
Any help is much appreciated.
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