What’s the expected number of HH in 10 consecutive coin tosses ? — Quantitative Problems on Probability
<p>First we will solve it using <strong>Recursion</strong>.</p>
<p>Let’s say E[n] = Expected number of HH in n consecutive tosses.<br />
Say X[i] = Output ( H/T ) on the <em>i</em>th toss.</p>
<p>If first toss returns T, then expected number of HH in 10 tosses is same as expected number of HH inthe next 9 tosses.<br />
E[10 | X[1] = T] = E[9].</p>
<p>If first toss returns H, then expected number of HH in 10 tosses is (1+E[9]) if 2nd toss returns H, and E[9] if 2nd toss returns T.</p>
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