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Further Stats Year 1
AS Further Maths- Edexcel
| Question | Answer |
|---|---|
| How do you work out E(X) of a discrete random variable? | Σ (x P(X=x)) |
| How do you work out E(X²) of a discrete random variable? | Σ (x² P(X=x)) |
| Var(X) = | E(X²) - E(X)² |
| E(aX+b) = | aE(X)+b |
| E(X+Y) = | E(X) + E(Y) |
| Var(aX+b) = | a²Var(X) |
| X~Po(λ). P(X=x) = | (e^-λ λ^x) / x! |
| 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 |
| X~Po(5), Y~Po(6), X+Y~Po(?) | 11 |
| X~Po(λ). E(X)= | λ |
| X~Po(λ). Var(X)= | λ |
| X~B(n,p). E(X)= | np |
| X~B(n,p). Var(X)= | np(1-p) |
| X~B(100,0.02) can be approximated by... because... | X~Po(2) as n is large and p is small |
| What are the hypothesise for a hypothesis test for the mean of a Poisson distribution? | H0- λ=(some value) H1- λ >/</≠ (some value) |
| How many critical regions/values does H1: λ > 3 have? | 1 region 1 value |
| How many critical regions/values does H1: λ ≠ 3 have? | 2 regions 2 values |
| 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 |
| What does a goodness of fit tell us? | How well an observed frequency fits to a known distribution |
| How do we calculate goodness of fit? | Σ (Oi² / Ei) - N |
| χ² can approximate X² as long as... | None of the expected values are below 5 |
| Degrees of freedom= | No. cells (after combining) - no. constraints |
| What are the 2 typical constraints? | 1) A limited sample was used 2) A value was calculated beforehand |
| What dictates which χ² you use? | Degrees of freedom |
| X² > χ² then... | reject H0 |
| X² < χ² then... | accept H0 |
| How do you work out expected values of a contingency table? | (row total x column total) / grand total |
| How do you work out degrees of freedom of a contingency table? | No. cells remaining after removing last row and column |
Created by:
XanderMoore
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