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see the picture below and finish it befure Due 11:59pm on Dec 10th.

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see the picture below and finish it befure Due 11:59pm on Dec 10th.

1. For a given shape S C R2, let c(S) =
Var(X) Var(Y)-Cov(X,Y)2
area(S)2
(a) Let S = (-1, 1)2. Determine c(S).
(b) Let S be the disk of radius 1. Determine c(S).
2. Describe a counterexample that shows that Markov's inequality does
not hold if the random variable can take negative values. More pre-
cisely, show that there exits a random variable X and a value a > 0
such that P(X > a) > E(X)/a.
3. Describe an example that shows that Chebyshev's inequality is tight.
Iore precisely, show that there exists a dom varial X and a value
€ > 0 such that P(|X – ul > €) = 02/62. (Optional hint: find first an
example that shows that Markov's inequality is tight)

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