AH Statistics Proofs (extension)

Proofs of some of the key formulas in Advanced Higher Statistics. Not required for the course but some pupils (and teachers) may find it interesting.

• proof the two ways of writing the variance formula are equivalent
• proof that using the ‘divide by n-1’ formula gives the best estimate of a population variance
• proof of Bayes Theorem
• proof of laws of expectation and variance
• proof of the origin of the Poisson formula, and of the mean and variance
• proof of mean and variance for uniform discrete
• proof of mean and variance for uniform continuous
• proof that using proportions and the normal approximation to a binomial are equivalent
• proof a line of best fit goes through the average point
• proof the line of best fit gives the least squares
• proof of SSR formula
• proof in bivariate analysis DF=n-2
• proof test slope parameter nonzero and coefficient of correlation nonzero are equivalent