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A Level Further Math, Edexcel: Further Statistics 1 With Solutions

Expected value E(X) - The mean of a probability distribution. E(X)=μ=∑xP(X=x)

Poisson distribution - A discrete probability distribution used to model the number of times an event occurs within a fixed period of time. X~Po(λ), is defined by the parameter λ. A Poisson model is suitable if events occur: independently; singly; at a constant average rate. The binomial distribution can be approximated by a Poisson distribution when n is large and p is small (np ≤ 10).

Geometric Distribution - A discrete probability distribution describing the number of trials needed to achieve a single success. Geo(p) defined by the parameter p, assuming that each trial is independent and has a constant probability of success.

Negative binomial distribution - A discrete probability distribution describing the number of trials needed to achieve a specified number of successes

Goodness of fit - A hypothesis test to determine whether a particular distribution is a suitable model ('good fit') for some observed data

contingency table - A two way table of catagorised frequencies used to test whether two particular attributes (or factors) of a population are associated.

Degrees of freedom - Number of free choices that can be made in the allocation of expected frequencies, calculated using:
number of degrees of freedom = number (n) of cells (after any combining) - number of constraints.

Constraint - Restrictions limiting the degrees of freedom in a Chi-squared test. Most Chi-squared tests have 1 constraint for each attribute caused by the frequency sum. An estimated parameter value for a binomial, geometric or Poisson distribution generates a further constraint.

Central limit theorem (CLT) - For a population with mean μ and variance σ^2, for large n
the distribution of sample means can be approximated by a normal distribution, regardless of the distribution of X. This relies on samples being random and independent. Note that where X is normally distributed the central limit theorem is not required.

Chi-squared distribution (Pearson's Chi-squared test) - A distribution used for a one-tailed test comparing observed with expected frequencies. The distribution for k degrees of freedom is the sum of the squares of k independent standard normal random variables. A chi-squared test evaluates whether differences between categories can be explained by chance.

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Level: University
School: Chamberlain College Of Nursing
Course: Math Models
Subject: math
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Section: Examinations
Made on: 12-29-2023
Type: .pdf
Pages: 2
Language: English

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