grandes-ecoles 2016 QIV.B.5

grandes-ecoles · France · centrale-maths1__psi Binomial Distribution Justify Binomial Model and State Parameters

Let $p \in ]0,1[$, $q = 1-p$, $m = n^2$. For $k \geqslant 1$, the number of modifications made during the $k$-th pass is denoted $N_k$.
Let $r \geqslant 1$ be an integer and $S_r = N_1 + \cdots + N_r$. What does $S_r$ represent? Give its distribution (you may use the previous question).

Let $p \in ]0,1[$, $q = 1-p$, $m = n^2$. For $k \geqslant 1$, the number of modifications made during the $k$-th pass is denoted $N_k$.

Let $r \geqslant 1$ be an integer and $S_r = N_1 + \cdots + N_r$. What does $S_r$ represent? Give its distribution (you may use the previous question).

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.C QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.A.5 QIV.A.6 QIV.A.7 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.B.6