Download Advanced Level Mathematics: Statistics 1 by Steve Dobbs PDF

By Steve Dobbs

Written to compare the contents of the Cambridge syllabus. data 1 corresponds to unit S1. It covers illustration of knowledge, diversifications and mixtures, chance, discrete random variables and the traditional distribution.

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Example text

If we want to minimize the squared error E[(X − e)2 ] = E[X 2 − 2eX + e2 ] = E(X 2 ) − 2eE(X) + e2 , differentiate to obtain 2e − 2E(X), which is zero at e = E(X). Example. Your friend throws a die and you have to estimate its value X. 5. What happens if you have additional information? Suppose that your friend will tell you the parity of the die value, that is, whether it is odd or even? How should we modify our guess to take this new information into 0 if X is even account? Let’s define the random variable P = .

0 1 2 ··· N − 1 N •....... ... . • 0 • 1 • 2 • ... N − 1 N Note. Any function g : S → R can also be considered as the column vector whose coordinates are the numbers g(x) for x ∈ S. Multiplying this vector on the right of the transition matrix P gives a new column vector (= function) P g with coordinates (P g)(x) = y∈S g(y)p(x, y). Definition.

A0 a1 a2 a3a4 1 .. ... .. ........ ........... . ... . ... ...

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