Quiz 2 solutions

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Let <m>N</m> be the number of heads in <m>n</m> coin flips with bias <m>p</m>.
Then <m>N\sim \Bin(n, p)</m>.
<md>
<mrow> \E)N) = \sum_{i=0}^n i\cdot b(i; n, p) = \sum_{i = 0}^n i \cdot {n \choose i} p^i (1-p)^{n - i}. </mrow>
<mrow> \E(N) = \sum_{i=0}^n i\cdot b(i; n, p) = \sum_{i = 0}^n i \cdot {n \choose i} p^i (1-p)^{n - i}. </mrow>
</md>
Gross.
</p>