grandes-ecoles 2015 QV.F

grandes-ecoles · France · centrale-maths1__psi Probability Definitions Almost Sure Convergence and Measure-Theoretic Probability
We assume $m>1$. Let $\alpha$ be the probability of extinction and $\beta$ be the probability that the sequence $(Y_n)$ diverges to infinity.
Show that $\alpha+\beta=1$. 
We assume $m>1$. Let $\alpha$ be the probability of extinction and $\beta$ be the probability that the sequence $(Y_n)$ diverges to infinity.

Show that $\alpha+\beta=1$.
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