Transducer Types and Their Applications

What is transducer? What are transducer types? Find out more about transducer types and their applications on HangOuter.

The Central Limit Theorem

The Central Limit Theorem or CLT in short says that the distribution of scaled random variable approaches a normal distribution.

The Weak Law of Large Numbers

According to law the sample mean \(\bar X\) of a large number of i.i.d.(independent identically distributed) random variables, with high probability, is very close to the mean, from a distribution for which it was taken.

Properties of Sample Mean

If we have sequence of random variables \(X_1, X_2, ... X_n\), we can define Sample Mean \(\bar X\) as their average: $$\bar X = {1 \over n}(X_1 + X_2 + ... + X_n)$$

Chebyshev Inequality

Says that the proability that X is far away from its mean, is bounded by quantity that increases as Var(X) increases.

Markov Inequality

Puts bound on how much probability can be at arbitrarily large values once its mean is specified: $$if \;\;P(X \ge 0) = 1 $$ then $$P(X \ge t) \le {E(X) \over t}, where ~t > 0$$