I'm not sure how to solve this problem:
C = random variable; the number of heads in 100 independent fair coin flips
Find E(C) and V(C).
Find the upper bounds on P(C >75), using Markov's Inequality and Tchebychev's Inequality.
I understand how to get E(C) (which I believe is 50), but I'm confused on how to complete the rest.
Best Answer
$C$ is distributed according to the binomial distribution with probability $p$, which I assume is $1/2$ in this case.
According to http://en.wikipedia.org/wiki/Binomial_distribution we have $E(C)=np$ which in your case is indeed 50. Furthermore, $V(C)=np(1-p)$.
You can use the Markov inequality $$P(X\geq a)\leq a^{-1} E(X)$$ to calculate an upper bound to $P(C>75)$ since you already know $E(C)$.