# Chebyshev's Inequality

Very important, with this base, some famous indicator spread widely much like Bollinger Bands and CCI.

#### Formula

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While

- X is the random variable
- E(X) is the expectation of the X
- Dev(X) is the deviation of the X
- Var(X) is the variance of X
- any real number k > 0
- any real number
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#### Where Could We Apply with Chebyshev's Inequality

This theory can apply to both Discrete and Continuous Random Variables.

That means it suits to the market price movement.

Trader can use it to predict the price movement.

Business man utilize it for decision.

#### How Chebyshev's Inequality Help Us in The Market

**First**, we need to know what we can achieve when we count out the result of this formula. The formula (1) tells us, the probability up bound is surely when you set the k value.

12 trader have the same $5,000 initiate fund. one month later, the average of their funds is $8,000, and the deviation is $4,500.

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We may know that at least 3(12 * 1/4) traders double their accounts.

**Second**, give a real example, the one we all familiar with, Bollinger Bands.