formula-sheet-1 - Formula sheet E (X ) = x x · p( x ) V (X...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Formula sheet E (X ) = x x · p( x ) V (X ) = E [(x − µ)2 ] = x n i=1 (Xi (x − µ)2 · p(x) = E (X 2 ) − [E (X )]2 n 2 ( Xi ) n i=1 ¯ X2 − − X )2 n S= = i=1 i n−1 n−1 If A1 , A2 , · · · , Ak be mutually exclusive and exhaustive events. Then for an event B, 2 k P (B ) = P (B |A1 )P (A1 ) + · · · + P (B |Ak )P (Ak ) = i=1 P (B |Ai )P (Ai ) P (Aj |B ) = Binomial Distribution: P (X = k ) = Poisson Distribution: P (Aj ∩ B ) = P (B ) P (B |Aj )P (Aj ) k i=1 P (B |Ai )P (Ai ) j = 1, · · · , k n! pk (1 − p)n−k , k !(n − k )! E (X ) = np , V (X ) = np(1 − p) P (X = k ) = Hypergeometric Distribution: λ k e− λ , k! E (X ) = V (X ) = λ , e = 2.718 P (X = k ) = M k N −M n−k N n . 1 ...
View Full Document

This note was uploaded on 02/15/2011 for the course SYSC 3600 taught by Professor Adsd during the Spring '10 term at Universidad Alfonso X El Sabio.

Ask a homework question - tutors are online