query: How to show that $\mathrm{mgf}$ $M(s)$ and $\mathrm{pgf}$ $P(s)$ are related?
positive_passages.docid: 157855
positive_passages.text: What is the difference between moment generating function and probability generating function?
negative_passages.docid: 111348
negative_passages.text: Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
negative_passages.docid: 28934
negative_passages.text: Presentation of SL$(n,\mathbb{Z}_p)$
negative_passages.docid: 53426
negative_passages.text: Proof of a formula involving Euler's totient function: $\varphi (mn) = \varphi (m) \varphi (n) \cdot \frac{d}{\varphi (d)}$
negative_passages.docid: 113612
negative_passages.text: Why does $P(\theta_1\mid D, \theta_2) \propto P(D \mid \theta_1, \theta_2)P(\theta_1)$ hold?
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
negative_passages.docid: 120985
negative_passages.text: Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
negative_passages.docid: 79165
negative_passages.text: How to show that $P(A\cup B) = P(A) + P(B) - P(A\cap B)$
negative_passages.docid: 137982
negative_passages.text: Show that $\textbf{ZF}$ shows $\phi$ is $\Delta_1$
negative_passages.docid: 46147
negative_passages.text: Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
negative_passages.docid: 133801
negative_passages.text: Finding the PGF of $Z$ using conditional expectation.
negative_passages.docid: 48291
negative_passages.text: Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
negative_passages.docid: 27735
negative_passages.text: Morphism to Projective Space $\mathbb{P}^m$
negative_passages.docid: 125188
negative_passages.text: how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
negative_passages.docid: 66089
negative_passages.text: Using AM-GM to prove $\lim_{p\to 0}$ of the $p$-mean is equal to the GM.
negative_passages.docid: 91935
negative_passages.text: If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
negative_passages.docid: 158583
negative_passages.text: Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.