Weak of large businesses.

0 N A = 2 0 -2 O 8 1. find the eigenvalues and obtain the orthogonal eigenvectors. 2. find the spectral decomposition of A. 3. find A-1 4. Prove that A1/2A-1/2 = A-1/2A1/2 = 1Markov inequality For a random variable X 2 0 with mean / > 0, and any numbert > 0: P (X > D). Note that the Markov inequality is restricted to non-negative random variables. Chebyshev inequality For a random variable X with (finite) mean / and variance of, and for any number t 2 0, P(X -/| 20) . Remark: When Markov inequality is applied to (X - ()", we obtain Chebyshev's inequality. Markov inequality is also used in the proof of Hoeffding's inequality. Hoeffding versus Chebyshev 4 points possible (graded) Let X1, X2, ..., X'n " Unif (0, b) be ni.i.d. uniform random variables on the interval [0, b] for some positive b. Suppose n is small (i.e. 7