Suppose n independent and BIASED coins are filpped. And the coins following the following pattern: The i th coin has probability i being heads, for i = 1, 2, 3, ..., n. H_n is a random variable that equal to the total number of heads. 1. What is the expected value of H_n? 2. What is the variance and the standard deviation of H_n? 3. Find a upper bound of the probability H_n 2 9n/10 with Markov's inequality. https://en.wikipedia.org/wiki/Markov's_inequality Statement [ edit ] If X is a nonnegative random variable and a > 0, then the probability that X is at least a is at most the expectation of X divided by a:[1] E(X) P(X Z a) S a Let a = a . E(X) (where a > 0); then we can rewrite the previous inequality as P(X 2 a . E(X))