22 lines
390 B
TeX
22 lines
390 B
TeX
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Important stuff not done in the lecture.
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Moments:
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$\bE[X^k]$
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\begin{lemma}
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Let $X, Y : \Omega \to [a,b]$
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If $\bE[X^k] = \bE[Y^k]$,
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for every $k \in \N_0$
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then $X = Y$.
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\end{lemma}
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\begin{proof}
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We have $\bE[p(X)] = \bE[p(Y)]$ for
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every polynomial $p$.
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Approximate $e^{\i t X}$
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with polynomials and use Fourier transforms.
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\end{proof}
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Laplace transforms
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