PSTAT 160A week 1 class 2

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6 Terms

1
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Given a random variable X, define the moment generating function

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2
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if X and Y are independent, how does the MGFX+Y(•) simplify?

MGFX(•) • MGFY(•)

similarly E(et(x+y)) = E(etx) • E(ety)

3
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obtain the mgf by differentiating

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4
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what is the power/taylor series defined as?

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5
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define the probability generating function

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6
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what is the formula for turning the PGF into a probability formula?

This process proves that the PGF and the probability distribution contain the exact same information. If PX​(t) is identical to PY​(t), then decoding them will produce the exact same set of probabilities. Therefore, X and Y must be identically distributed.

<p>This process proves that the PGF and the probability distribution contain the <strong>exact same information</strong>. If <span>PX</span>​(t) is identical to <span>PY</span>​(t), then decoding them will produce the exact same set of probabilities. Therefore, X<span> </span>and Y<span>&nbsp;</span>must be identically distributed.</p>