2. Let $X_1, X_2, \dots$ be a sequence of independent identically distributed continuous random variables. We say that a record occurs at time $n$ if $X_n > \max(X_1, \dots, X_{n-1})$. That is, $X_n$ is a record if it is larger than each of $X_1, \dots, X_{n-1}$. Show that $P[\text{a record occurs at time } n] = \frac{1}{n}$
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A record occurs at time \( n \) if \( X_n > \max(X_1, X_2, \ldots, X_{n-1}) \). Show more…
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