AS Further Maths- Edexcel
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| How do you work out E(X) of a discrete random variable? | Σ (x P(X=x))
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| How do you work out E(X²) of a discrete random variable? | Σ (x² P(X=x))
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| Var(X) = | E(X²) - E(X)²
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| E(aX+b) = | aE(X)+b
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| E(X+Y) = | E(X) + E(Y)
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| Var(aX+b) = | a²Var(X)
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| X~Po(λ). P(X=x) = | (e^-λ λ^x) / x!
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| What are the three condition needed for the Poisson distribution to be suitable? | Events occur: independently, singly (in space or time), at a constant average rate
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| X~Po(5), Y~Po(6), X+Y~Po(?) | 11
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| X~Po(λ). E(X)= | λ
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| X~Po(λ). Var(X)= | λ
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| X~B(n,p). E(X)= | np
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| X~B(n,p). Var(X)= | np(1-p)
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| X~B(100,0.02) can be approximated by... because... | X~Po(2) as n is large and p is small
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| What are the hypothesise for a hypothesis test for the mean of a Poisson distribution? | H0- λ=(some value)
H1- λ >/</≠ (some value)
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| How many critical regions/values does H1: λ > 3 have? | 1 region 1 value
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| How many critical regions/values does H1: λ ≠ 3 have? | 2 regions 2 values
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| What are the typical hypothesise for a chi sqaured test? | H0- There is no difference between the observed and the theoretical distribution
H1- There is a difference between the observed and the theoretical distribution
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| What does a goodness of fit tell us? | How well an observed frequency fits to a known distribution
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| How do we calculate goodness of fit? | Σ (Oi² / Ei) - N
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| χ² can approximate X² as long as... | None of the expected values are below 5
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| Degrees of freedom= | No. cells (after combining) - no. constraints
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| What are the 2 typical constraints? | 1) A limited sample was used
2) A value was calculated beforehand
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| What dictates which χ² you use? | Degrees of freedom
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| X² > χ² then... | reject H0
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| X² < χ² then... | accept H0
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| How do you work out expected values of a contingency table? | (row total x column total) / grand total
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| How do you work out degrees of freedom of a contingency table? | No. cells remaining after removing last row and column
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Created by:
XanderMoore
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