9 Convergence in probability
P(|Yn −a| ≤ ǫ) converges to 1, for any fixed ǫ > 0. This is equivalent to P(|Yn −a| > ǫ) → 0 as n → ∞, again for any fixed ǫ > 0. Example 9.1. Toss a fair coin n times, independently. Let Rn be the “longest run of heads,” i.e., the longest sequence of consecutive tosses of Heads. For example, if n = 15 and the tosses come out ................
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