grandes-ecoles 2020 Q19

grandes-ecoles · France · mines-ponts-maths2__mp_cpge Discrete Probability Distributions Recurrence Relations and Sequences Involving Probabilities

Let $n \in \mathbb{N}^{*}$. Show that $$1 = \sum _ { k = 0 } ^ { n } P \left( S _ { k } = 0 _ { d } \right) P ( R > n - k )$$

Let $n \in \mathbb{N}^{*}$. Show that
$$1 = \sum _ { k = 0 } ^ { n } P \left( S _ { k } = 0 _ { d } \right) P ( R > n - k )$$