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Copy file name to clipboardexpand all lines: Lecture_17.ipynb
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"\n",
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"Let $X$ have MGF $M(t)$.\n",
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"\n",
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"1. The $n$-th moment $\\mathbb{E}(X^{n})$ is the coeficient of $\\frac{t^{n}}{n!}$ in the Taylor series of $M$, i.e., $M^{n}(0) = \\mathbb{E}(X^{n})$\n",
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"1. The $n$-th moment $\\mathbb{E}(X^{n})$ is the coefficient of $\\frac{t^{n}}{n!}$ in the Taylor series of $M$, i.e., $M^{n}(0) = \\mathbb{E}(X^{n})$\n",
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"1. MGF determines the distribution, i.e., if $X$ and $Y$ have the same MGF, then they have the same CDF\n",
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"1. sums of random variables (convolutions) are difficult; but if we have MGFs, they are _easy_\n",
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