grandes-ecoles 2015 QII.C.2

grandes-ecoles · France · centrale-maths1__psi Poisson distribution

During a laying, an insect lays a random number of eggs following a Poisson distribution with parameter $\lambda>0$. Then, the probability that a given egg becomes a new insect is $\alpha\in]0,1[$.
Using the composition relation $G_S=G_T\circ G_X$, determine the distribution of the number of insects resulting from the laying.

During a laying, an insect lays a random number of eggs following a Poisson distribution with parameter $\lambda>0$. Then, the probability that a given egg becomes a new insect is $\alpha\in]0,1[$.

Using the composition relation $G_S=G_T\circ G_X$, determine the distribution of the number of insects resulting from the laying.

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