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Chernoff Bounds
Chernoff Bounds
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Intermediate
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2 intermediate
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Question 1 of 3
120s
intermediate (4/10)
conceptual
In the Chernoff method, to bound
P
(
X
≥
t
)
you write
P
(
X
≥
t
)
≤
in
f
λ
>
0
e
−
λ
t
E
[
e
λ
X
]
. What is the role of the optimization over
λ
?
Hide and think first
A.
It upgrades a one-sided tail bound into a symmetric two-sided concentration bound
B.
It is a mathematical formality since any fixed
λ
>
0
gives the same asymptotic rate
C.
Each
λ
>
0
gives a valid Markov bound, and the infimum picks the tightest one
D.
It guarantees the MGF converges, since without the infimum the upper bound could be infinite
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