grandes-ecoles 2019 Q30

grandes-ecoles · France · centrale-maths2__mp Continuous Probability Distributions and Random Variables Characteristic/Moment Generating Function Derivation

Using the result of Q29, propose another proof of the result obtained in question 6, i.e., the pointwise limit of the sequence of functions $(\varphi_n)_{n \geqslant 1}$ defined by $$\forall n \in \mathbb{N}^{\star}, \quad \varphi_n(t) = \mathbb{E}(\cos(t X_n)).$$

Using the result of Q29, propose another proof of the result obtained in question 6, i.e., the pointwise limit of the sequence of functions $(\varphi_n)_{n \geqslant 1}$ defined by
$$\forall n \in \mathbb{N}^{\star}, \quad \varphi_n(t) = \mathbb{E}(\cos(t X_n)).$$

Paper Questions

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