grandes-ecoles 2016 QIV.B.6

grandes-ecoles · France · centrale-maths1__psi Discrete Random Variables Expectation and Variance via Combinatorial Counting

Let $p \in ]0,1[$, $q = 1-p$, $m = n^2$. We denote by $N$ the smallest index $k$ for which the matrix $M_k$ is completely filled.
a) Propose an approach to approximate the expectation of $N$ using a computer simulation with the functions above.
b) Give an expression for the exact value of this expectation involving $q$ and $m$.

Let $p \in ]0,1[$, $q = 1-p$, $m = n^2$. We denote by $N$ the smallest index $k$ for which the matrix $M_k$ is completely filled.

a) Propose an approach to approximate the expectation of $N$ using a computer simulation with the functions above.

b) Give an expression for the exact value of this expectation involving $q$ and $m$.

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