Let $\ell > 0$ be fixed. Determine the behaviour of $\mathbb{E}(N(x, x+\ell))$ when $x \rightarrow +\infty$. Interpret the result. Is this result true if there exists $d > 0$ such that $\mathbb{P}(X \in d\mathbb{Z}) = 1$?
Let $\ell > 0$ be fixed. Determine the behaviour of $\mathbb{E}(N(x, x+\ell))$ when $x \rightarrow +\infty$. Interpret the result. Is this result true if there exists $d > 0$ such that $\mathbb{P}(X \in d\mathbb{Z}) = 1$?