Let $X$ be exponentially distributed with parameter $\lambda$. Find $\mathbb{P}(\textrm{sin}\:X>\frac{1}{2})$.
Tried a few times to integrate this, but can't get to the final result.
2026-03-31 07:48:51.1774943331
$\mathbb{P}(\textrm{sin}\:X>\frac{1}{2})$ if $X$ is exponentially distributed with parameter $\lambda$
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Hint: First find $\{x \ge 0: \sin(x) > 1/2\}$. This is the union of a sequence of intervals. Find the probability of each, and then sum a geometric series.