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Y Dosraniad Binomial

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Y Dosraniad Binomial. Cymedr ac amrywiant Dosraniad Binomial. X ~ B ( n , p ). Cymedr yr hapnewidyn yw gwerth disgwyliedig X. E(X) = np. Amrywiant yr hapnewidyn X Var (X) = npq (q = 1 - p). Y Gwyriad Safonol √Var (X) = √(npq) (q = 1 - p). Enghraifft

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slide1
Y Dosraniad Binomial

Cymedr ac amrywiant Dosraniad Binomial

X ~ B ( n , p )

Cymedr yr hapnewidyn yw gwerth disgwyliedig X.

E(X) = np

Amrywiant yr hapnewidyn X

Var (X) = npq (q = 1 - p)

Y Gwyriad Safonol

√Var (X) = √(npq) (q = 1 - p)

slide2
Enghraifft
  • Mae gan X ddosraniad Binomial lle mae’r nifer yn 30 a’r tebygolrwydd o lwyddiant yn 0.4.
  • Darganfyddwch
  • y cymedr,
  • y gwyriad safonol, cymedr ac amrywiant Y pan mae
  • Y = 3X + 4

X ~ B ( 30 , 0.4 )

a) E(X)

= np

= 30 x 0.4

= 12

b) √Var (X) =

√npq

= √(30 x 0.4 x 0.6)

= √7.2

= 2.68

slide3
X ~ B ( 30 , 0.4 )

= 3E(X) + 4

= 3 x 12 + 4

= 40

c) E(Y) = E(3x + 4)

Var(Y) = Var(3x + 4)

= 32 Var(X)

= 9 x 7.2

= 64.8

Ymarfer 4.5c

Mathemateg - Ystadegaeth Uned S1 – CBAC

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