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Analysis

T_BS = 4n + T_ISn + 3

Let n_i = number of elements in bucket B[i].

The expected time to sort elements in B[i] = E(O(n_i²)) = O(E(n_i²)).

Note that the expected value of a random variable X as described in Chapter 6, is

$\begin{displaymath}E(X) \;=\; \sum_x x Pr(X=x)\end{displaymath}$

The variable x here represents the value of X, and Pr(X=x) represents the probability that the value of X is x.

The variance of a random variable X with mean E[X] is notated Var[X].

E[X²] = Var[X] + E²[X]
P(X=k) = $\left(\!\! \begin{array}{c} n \\ [1ex] k \end{array} \!\! \right) p^k q^{n-k}$ This is the binomial distribution for n trials.

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