BBy Bot
Jun 09'24
Exercise
[math]
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Suppose that a gambler starts with a stake of 0 dollars.
- Show that the probability that her stake never reaches [math]M[/math] before returning to 0 equals [math]1 - p(1 - q_1)[/math].
- Show that the probability that her stake reaches the value [math]M[/math] exactly [math]k[/math] times before returning to 0 equals [math]p(1-q_1)(1 - qq_{M-1})^{k-1}(qq_{M-1})[/math]. Hint: Use Exercise.