grandes-ecoles 2015 QIV.D.3

grandes-ecoles · France · centrale-maths1__mp Continuous Probability Distributions and Random Variables Change of Variable and Integral Evaluation

We consider a function $f$ in $\mathcal{B}_1$ such that $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ are in $\mathcal{B}_2$. The Radon inversion formula states: $\forall (x,y) \in \mathbb{R}^2,\ f(x,y) = \frac{-1}{\pi} \int_0^{+\infty} \frac{R_{x,y}^{\prime}(q)}{q}\,\mathrm{d}q$.
Propose a method to obtain the Radon inversion formula at any pair $(x,y)$ from the formula at $(0,0)$.

We consider a function $f$ in $\mathcal{B}_1$ such that $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ are in $\mathcal{B}_2$. The Radon inversion formula states: $\forall (x,y) \in \mathbb{R}^2,\ f(x,y) = \frac{-1}{\pi} \int_0^{+\infty} \frac{R_{x,y}^{\prime}(q)}{q}\,\mathrm{d}q$.

Propose a method to obtain the Radon inversion formula at any pair $(x,y)$ from the formula at $(0,0)$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.C.1 QI.C.2 QI.C.3 QI.C.4 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QIII.A QIII.B QIII.C.1 QIII.C.2 QIII.C.3 QIV.A.1 QIV.A.2 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QIV.D.3 QV.A.1 QV.A.2 QV.A.3 QV.B.1 QV.B.2