Sums of independent random variables

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Reference no: EM131824554

Sums of independent random variables.

a) Show that for any random variables X, Y , and Z,

E(X + Y + Z) = E(X) + E(Y ) + E(Z) .

b) Show that for independent random variables X, Y , and Z,

Var(X + Y + Z) = Var(X) + Var(Y ) + Var(Z) .

c) Generalize these results to sums of n random variables.

d) Do we need full independence for the variance of a sum to be the sum of the variances, or is pairwise independence sufficient?

Reference no: EM131824554

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