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A uniform random variable on (0,1), X, has density function f(x) = 1, 0 < x...

A uniform random variable on (0,1), X, has density function f(x) = 1, 0 < x < 1. Let Y = X1 + X2 where X1 and X2 are independent and identically distributed uniform random variables on (0,1).

1) By considering the cumulant generating function of Y , determine the first three cumulants of Y .

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Answer #1

k3 is 1/2-1+1/2=0

So k1=1

K2=1/6

K3=0

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