S2 Conditions

  • Created by: Audrey
  • Created on: 19-02-17 11:38
Conditions for Binomial Distribution X ~ B(n, p)
1)A single trial has exactly two possible outcomes (success and failure) 2)This trial is repeated a fixed number, n, times. 3)The n trials are independent. 4)The probability of success (p) remains the same for each trial
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Conditions for a Poisson distribution X ∼ Po (λ)
1) Two events cannot occur at the same time 2)uniformly (In a way that is the same in all cases and at all times) 3)independently 4)mean=variance 5) "rate" "per week"
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Conditions for The Poisson as an approximation to the binomial
1) If in the Binomial distribution B(n, p) p is ‘small’ and n is ‘large’, then we can approximate by a Poisson distribution with mean λ = np, Po(np). 2)In practice we use this approximation when p is small and np ≤ 10,
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Conditions for Continuous random variables
1) total area is ONE 2) the curve never goes below the x-axis 3) probability that X lies between a and b is the area from a to b 4) Outside the interval shown, f (x) = 0 and this must be shown on any sketch. 5)
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Conditions for Continuous uniform (rectangular) distribution
A continuous uniform distribution has constant probability density over a fixed interval.
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Conditions for Normal approximation
1) If p is ‘near’ 0.5 and if n is large, np > 10, then the normal distribution N(np, npq) can be used as an approximation to the binomial.
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Card 2

Front

Conditions for a Poisson distribution X ∼ Po (λ)

Back

1) Two events cannot occur at the same time 2)uniformly (In a way that is the same in all cases and at all times) 3)independently 4)mean=variance 5) "rate" "per week"

Card 3

Front

Conditions for The Poisson as an approximation to the binomial

Back

Preview of the front of card 3

Card 4

Front

Conditions for Continuous random variables

Back

Preview of the front of card 4

Card 5

Front

Conditions for Continuous uniform (rectangular) distribution

Back

Preview of the front of card 5
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