IE 300/GE 331 Lecture 19
Negar Kiyavash, UIUC
1
Probability Inequalities:
•
Markov inequality:
X is nonnegative r.v., then for any a>0:
•
Chebyshev inequality: If X is an r.v. with mean
μ
and variance
σ
2,
then
Important trick:
If we
cannot
calculate variance of a finite ranged
r.v (it takes values in the range [a,b]), then we can use the
bound V[X] <= (ba)
2
/4
.
]
[
)
(
P
a
X
E
a
X
≤
≥
.
)

(
P
2
2
c
c
X
σ
μ
≤
≥
−
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