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What is the probability that $X=x$ using its PGF?

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Remember that $P_X(s) = \\mbox{E}[s^X] = \\sum_Kp_ks^k$ so to find $p_x$ you need to:

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    \n
  1. Derive $x$ times so it is the only value without an $s$
  2. \n
  3. Evaluate at $s=0$ so it is the only remaining term
  4. \n
  5. Divide by $x!$ to account for the constant introduced during the derivatives
  6. \n
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