Catherine Palmer

Linear combinations of $2 \times 2$ matrices. Three examples.

The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

Multiplication of $2 \times 2$ matrices.

Financial Mathematics  

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Calculate confidence interval for the proportion

Calculate confidence interval for the mean, sample variance n>30

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Calculate confidence interval for the mean, sample variance adaptive marking

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

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rebelmaths

Printing errors in the work produced by a particular film occur randomly at an average rate of p per page.

i.What is the probability that a one page document will contain x1 printing error(s)?

ii.If a n page document is printed, calculate the probability of having more than x2 errors. Assume a Poisson distribution.

Add, subtract, multiply and divide algebraic fractions.

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Provided with information on a sample with sample mean and known population variance, use the z test to either or reject a given null hypothesis. One sided.

Provided with information on a sample (>30) with sample mean and standard deviation, use the z test to either accept or reject a given null hypothesis.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.