Don't Expect The Expectation
Toss 51 fair coins.
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What is the expected number of heads? Please answer in the form of a decimal.
Let \(X\) be the number of heads. Then \(X\) has a binomial distribution, where \(E[X]=np=51\cdot\frac{1}{2}=25.5\) -
What is the probability of getting exactly 25 heads? Please answer in the form of a decimal with 4 significant digits.
Let \(X\) be as above. Then \(\Pr[X=25]=PDF_X(25)=\binom{51}{25}\cdot\frac{1}{2^{51}}\)