grandes-ecoles 2022 Q27

grandes-ecoles · France · centrale-maths2__psi Continuous Probability Distributions and Random Variables Integrability, Boundedness, and Regularity of Density/Distribution-Related Functions
We fix two functions $f$ and $g$ in $E$. For $x > 0$, we set $F ( x ) = - U ( f ) ^ { \prime } ( x ) \mathrm { e } ^ { - x }$. Show the existence and calculate the values of the limits at $0$ and at $+ \infty$ of the function $t \mapsto F ( t ) U ( g ) ( t )$. 
We fix two functions $f$ and $g$ in $E$. For $x > 0$, we set $F ( x ) = - U ( f ) ^ { \prime } ( x ) \mathrm { e } ^ { - x }$. Show the existence and calculate the values of the limits at $0$ and at $+ \infty$ of the function $t \mapsto F ( t ) U ( g ) ( t )$.
Paper Questions
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