grandes-ecoles 2016 QIV.B.4

grandes-ecoles · France · centrale-maths1__psi Geometric Distribution
Let $p \in ]0,1[$, $q = 1-p$, $m = n^2$. The smallest integer $k \geqslant 1$ such that the coefficient at row $i$, column $j$ of $M_k$ equals 1 is denoted $T_{i,j}$.
For an integer $k \geqslant 1$, give the value of $P(T_{i,j} \geqslant k)$.
Let $p \in ]0,1[$, $q = 1-p$, $m = n^2$. The smallest integer $k \geqslant 1$ such that the coefficient at row $i$, column $j$ of $M_k$ equals 1 is denoted $T_{i,j}$.

For an integer $k \geqslant 1$, give the value of $P(T_{i,j} \geqslant k)$.