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Solution. Any diagonal n n matrix looks like 0 BBB BBB BBB B@ a1 an 1 CCC CCC CCC CA = a1E11 + + anEnn where Eii is the matrix with entries all 0 except a 1 at the i’th diagonal entry. This tells us that (E11; ;Enn)is a basis because these n matrices are already independent as in Rnn.The dimension is n. 4.1.24 Find a basis of the space of all upper triangular 3 3 matrices and determine its ...

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and more generally M(n)(0) = E(Xn), n ≥ 1.(8) The mgf uniquely determines a distribution in that no two distributions can have the same mgf. So knowing a mgf characterizes the distribution in question.

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