Question

A. (i) Consider the random variable X with pmf: pX (−1) = pX (1) = 1/8,...

A. (i) Consider the random variable X with pmf: pX (−1) = pX (1) = 1/8, pX (0) = 3/4.

Show that the Chebyshev inequality P (|X − μ| ≥ 2σ) ≤ 1/4 is actually an equation for

this random variable.
(ii) Find the pmf of a different random variable Y that also takes the values {−1, 0, 1}

for which the Chebyshev inequality P (|X − μ| ≥ 3σ) ≤ 1/9 is actually an equation.

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