Markov's Inequality 마르코프 부등식

Markov's Inequality 

Markov's Inequality is one of the most important and basic Inequalities. 

You can find the upper bound of probability that nonnegative random variable(X) is equal or greater than a positive constant(C).

<Markov's Inequality of X> 

P(X≥C) ≤ E(X)/C

X: nonnegative random variable 

C: any positive constant

<Proof>

Let me give you the proof 

<Generalization>

<EXAMPLE>

<Markov's Inequality of g(X)> 

P(g(X)≥C) ≤ E(g(X))/C

g(X): nonnegative function 

C: any positive constant

<Proof>

<Generalization>