Many binomial tables only tabulate symmetries up to 0.5. This does not mean we cannot use the binomial tables for any value of p greater than 0.5 – only that some manipulation is involved. The manipulation rests on thatrepresents the probability of success in most textbooks.then represents the probability of failure. Ifthenand we can use […]

## Sums of Poisson Distributions

If a random variable has a Poisson distribution, so that in some sense, events occur at a certain rate, then we can scale the distribution, so that the interval over which events occur changes. If print errors occur at the rate of three per page, then they occur at the rate of one per third […]

## The Uniform Distribution

If a probability distribution is such that any value between two limitsis equally likely then the uniform distribution,may be suitable. The Uniform distribution may be either continuous eg sometime in the next hour the postman will arrive, or discrete eg the score on a fair dice. The mean of the Uniform distribution is the midpoint […]

## Finding the Median of a Continuous Random Distribution

The median of a distributioin is the ‘half way’ point, such that the probability of observing a value less than the median equals the probability of observing a value greater than the medianThis is illustrated below. Concisely we solvewhereis the lower limit of the range of Example: Find the median of the distribution given by

## Significance Levels and p – Values

When conducting a hypothesis test, the criterion for rejecting the null hypothesis is that an observed value is so unlikely assuming that the null hypothesis is true that it must in fact be true. To decide this, each hypothesis test is associated with a significance level and the observed value must be less likely than […]

## What is a Statistic?

A statistic is a single measure of some attribute of a sample e.g. the mean. It is calculated by applying a function to the set of data. More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample’s distribution; that is, the function can […]

## Conditions for a Distribution to be Modelled by a Normal Distribution

The normal distribution is the most useful and widely used statistical distribution, but it can’t be used everywhere. When considering whether or not a distribution can be modelled by the normal distribution we should keep in mind the main features of the normal distribution: It is a bell shaped curve symmetrical about the mean. It […]

## The Normal Approximation to The Geometric Distribution and the Continuity Correction

The geometric distribution, writtenhas Expectation ValueThe variance is given byIf we want to use the normal distribution as an approximation to estimatefor example we must make modifications since the binomial distribution is a discrete distribution but the normal approximation is continuous. In order to take account of this, and that if we are estimatingmay be […]

## Testing for Goodness of Fit to a Poisson Distribution by Comparing Variance With Mean

Typically raw data that may possibly be fitted by a Poisson distribution comes summarised in a frequency table. The table below contains data that shows the numbers of errors per page made by a secretary, and the associated frequencies. No. of errors 0 1 2 3 4 5 No. of Pages 37 65 60 49 […]

## One or Two Tailed Hypothesis Tests? Discussion

Hypothesis tests take one of two forms: One Tailed Tests – A claim is involved, or there is suspicion that the frequency, mean or proportion has increased or decreased. For example, a manufacturer of cat food claim 8 out of ten cats prefer his company’s cat food to any other company, or a new safety […]