Let be independent zero-mean real valued variables and let Then

Continue reading “Hoeffding’s Inequality”

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# Tag: Inequality

# Hoeffding’s Inequality

# Expectation: Useful properties and inequalities

# Rio’s Inequality

# Kolmogorov’s Maximal Inequality

Let be independent zero-mean real valued variables and let Then

Continue reading “Hoeffding’s Inequality”

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If is a random variable on . The expected value of is defined as

**Inequalities**

*Jensen’s inequality*. If is convex and

*Holder’s inequality*. If with then

*Cauchy-Schwarz Inequality*: For

Continue reading “Expectation: Useful properties and inequalities”

Let and be two integrable real-valued random variables and let be the quantile function of . Then if is integrable over we have

where is the a-mixing coefficient.

* Proof:* Set and then

since and

note also that

which implies that

- Let be independent random variables with . Set . Then
*Proof:*LetNotice that and