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formula-sheet-1

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

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Unformatted text preview: Formula sheet E (X ) = x x Â· p( x ) V (X ) = E [(x âˆ’ Âµ)2 ] = x n i=1 (Xi (x âˆ’ Âµ)2 Â· p(x) = E (X 2 ) âˆ’ [E (X )]2 n 2 ( Xi ) n i=1 Â¯ X2 âˆ’ âˆ’ X )2 n S= = i=1 i nâˆ’1 nâˆ’1 If A1 , A2 , Â· Â· Â· , Ak be mutually exclusive and exhaustive events. Then for an event B, 2 k P (B ) = P (B |A1 )P (A1 ) + Â· Â· Â· + P (B |Ak )P (Ak ) = i=1 P (B |Ai )P (Ai ) P (Aj |B ) = Binomial Distribution: P (X = k ) = Poisson Distribution: P (Aj âˆ© B ) = P (B ) P (B |Aj )P (Aj ) k i=1 P (B |Ai )P (Ai ) j = 1, Â· Â· Â· , k n! pk (1 âˆ’ p)nâˆ’k , k !(n âˆ’ k )! E (X ) = np , V (X ) = np(1 âˆ’ p) P (X = k ) = Hypergeometric Distribution: Î» k eâˆ’ Î» , k! E (X ) = V (X ) = Î» , e = 2.718 P (X = k ) = M k N âˆ’M nâˆ’k N n . 1 ...
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