(COMP233) Probability and Statistics -Marcov Inequality, Chebyshev's Theorem, Conditional Probability and Bayes's Rule

 

Marcov's Inequality 

: For a continuous nonnegative random variable X, and c>0, then 

* One of the application of E(x)*

 

Chebyshev's Theorem

: a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that lie must within one, two, or more standard deviations of the mean.

 

Conditional Probability

 

P(A | B) =  P(A and B) / P(B)

: a measure of an event occuring, given that another event has already occurred. 

 

Bayes's Theorem

->  It helps us to calculate conditional probability of an event if basically we know reverse conditional probability with some other probability values