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Further Statistics 1 formulae
The 16 results the Further Statistics 1 notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 16, the formulae booklet prints 13 and 3 are yours to memorise.
Further Maths · 7 lessons with formulae.
A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.
E(X) = Σ x P(X = x)E(X) = Σ x P(X = x) IN THE FORMULAE BOOKLETConditionsX discrete, summed over every value in its range, and the sum must converge. Var(X) = Σ x2 P(X = x) - μ2Var(X) = Σ x^2 P(X = x) - μ^2 IN THE FORMULAE BOOKLETConditionsX discrete with μ = E(X), and E(X²) must exist. P(X = x) = e-λ λxx!, E(X) = Var(X) = λP(X = x) = e^(-λ) (λ^x/x!), E(X) = Var(X) = λ IN THE FORMULAE BOOKLETConditionsEvents occurring singly, independently and at a constant average rate λ > 0; x = 0, 1, 2, … P(X = x) = p(1 - p)x-1, μ = 1p, σ2 = 1 - pp2P(X = x) = p(1 - p)^(x - 1), μ = (1/p), σ^2 = (1 - p)/p^2 IN THE FORMULAE BOOKLETConditionsIndependent trials with constant p, 0 < p ≤ 1, X counting the trial of the first success; x = 1, 2, 3, … P(X = x) = x-1Cr-1 pr(1 - p)x-rP(X = x) = ^(x - 1)C_(r - 1) p^r(1 - p)^(x - r) IN THE FORMULAE BOOKLETConditionsIndependent trials with constant p, X counting the trial of the rth success; x = r, r + 1, … μ = rp, σ2 = r(1 - p)p2μ = (r/p), σ^2 = (r(1 - p))/p^2 IN THE FORMULAE BOOKLETConditionsThe negative binomial above, with p > 0. sample mean ≈ N(μ, σ2n)sample mean ≈ N(μ, (σ^2/n)) IN THE FORMULAE BOOKLETConditionsA random sample of n independent, identically distributed observations with a finite mean and variance, and n large. The parent distribution need not be normal. χ2 = Σ (Oi - Ei)2Eiχ^2 = Σ (((O_i - E_i)^2)/E_i) IN THE FORMULAE BOOKLETConditionsExpected frequencies all at least 5, pooling classes where they are not, and the observations independent. Eij = row total × column totalgrand totalE_ij = (row total × column total)/grand total NOT IN THE BOOKLET: LEARN ITConditionsComputed under the null hypothesis that the two classifications are independent; each expected frequency should be at least 5. χ2 = Σ (Oi - Ei)2Eiχ^2 = Σ (((O_i - E_i)^2)/E_i) IN THE FORMULAE BOOKLETConditionsExpected frequencies all at least 5, pooling classes where they are not, and the observations independent. χ2 = Σ (|O - E| - 0.5)2Eχ^2 = Σ (((|O - E| - 0.5)^2)/E) NOT IN THE BOOKLET: LEARN ITConditionsYates' correction, for a contingency table with two rows and two columns and therefore one degree of freedom; expected frequencies at least 5. A larger table takes the uncorrected statistic. G(t) = E(tX) = Σ tx P(X = x)G(t) = E(t^X) = Σ t^x P(X = x) IN THE FORMULAE BOOKLETConditionsX taking non-negative integer values, with the series convergent, which it is for |t| ≤ 1. Var(X) = G''(1) + G'(1) - [G'(1)]2Var(X) = G′′(1) + G′(1) - [ G′(1)]^2 IN THE FORMULAE BOOKLETConditionsG differentiable twice at t = 1, so the mean and variance must exist. B(n, p): (q + pt)n, Po(λ): eλ(t - 1)B(n, p): (q + pt)^n, Po(λ): e^(λ(t - 1)) IN THE FORMULAE BOOKLETConditionsB(n, p) with q = 1 − p; Po(λ) with λ > 0. Geo(p): pt1 - qt, Neg B(r, p): (pt1 - qt)rGeo(p): (pt/(1 - qt)), Neg B(r, p): (pt/(1 - qt))^r IN THE FORMULAE BOOKLETConditionsq = 1 − p, and |qt| < 1 for the series to converge. Every formula in the library is indexed by unit on the equation index, and the Further Statistics 1 notes are where these results are derived and used. The 3 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.
Also: Further Pure 1 formulae · Further Pure 2 formulae