Question 8.2.7: If X is a random variable with mean µ ≠ 0 and variance σ², d......
If X is a random variable with mean µ ≠ 0 and variance σ2, define the relative deviation D of X from its mean by
D=\left|\frac{X-\mu }{\mu }\right|
(a) Show that P(D ≥ a) ≤ σ2 /(µ2a2 ).
(b) If X is the random variable of Exercise 1, find an upper bound for P(D ≥.2), P(D ≥ .5), P(D ≥ .9), and P(D ≥ 2).
(b) 1, 1, 100/243, 1/12
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