grandes-ecoles 2015 QIV.B

grandes-ecoles · France · centrale-maths1__psi Probability Generating Functions Branching process and extinction probability via PGF iteration
We assume that, for all $k\in\mathbb{N}$, $p_k=\frac{1}{2^{k+1}}$.
Verify that, for all $t\in\left[0,1\left[$, $\varphi_n(t)\neq 1$. 
We assume that, for all $k\in\mathbb{N}$, $p_k=\frac{1}{2^{k+1}}$.

Verify that, for all $t\in\left[0,1\left[$, $\varphi_n(t)\neq 1$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.B QI.C QI.D.1 QI.D.2 QI.E.1 QI.E.2 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.A.5 QII.B QII.C.1 QII.C.2 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.C.1 QIII.C.2 QIII.C.3 QIV.A QIV.B QIV.C QIV.D QIV.E QIV.F QIV.G QV.A QV.B.1 QV.B.2 QV.C.1 QV.C.2 QV.D.1 QV.D.2 QV.E QV.F