grandes-ecoles 2015 QV.E

grandes-ecoles · France · centrale-maths1__psi Probability Definitions Almost Sure Convergence and Measure-Theoretic Probability

Let $(A_n)_{n\in\mathbb{N}}$ be a sequence of events all with probability 1.
Show that $P\left(\bigcup_{n\in\mathbb{N}}\overline{A_n}\right)=0$. What can be deduced for $P\left(\bigcap_{n\in\mathbb{N}}A_n\right)$?

Let $(A_n)_{n\in\mathbb{N}}$ be a sequence of events all with probability 1.

Show that $P\left(\bigcup_{n\in\mathbb{N}}\overline{A_n}\right)=0$. What can be deduced for $P\left(\bigcap_{n\in\mathbb{N}}A_n\right)$?

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