4.6 Deviation: Markov & Chebyshev Bounds

Don't Expect The Expectation


Toss 51 fair coins.

  1. What is the expected number of heads? Please answer in the form of a decimal.

    Exercise 1

    Let \(X\) be the number of heads. Then \(X\) has a binomial distribution, where \(E[X]=np=51\cdot\frac{1}{2}=25.5\)

  2. What is the probability of getting exactly 25 heads? Please answer in the form of a decimal with 4 significant digits.

    Exercise 2

    Let \(X\) be as above. Then \(\Pr[X=25]=PDF_X(25)=\binom{51}{25}\cdot\frac{1}{2^{51}}\)