LSD and Tukey yardsticks on five treatments. Also two-way Anova test on same set of data.

Paired t-test to see if there is a difference between times take in a task.

Arrivals given by exponential distribution, parameter $\theta$ and $Y$, sample mean on inter-arrival times. Find and calculate unbiased estimator for $\theta$.

Independent events in probability. Choose whether given three given pairs of events are independent or not.

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

Given data on probabilities of three levels of success of three options and projections of the profits that the options will accrue depending on the level of success, find the expected monetary value (EMV) for each option and choose the one with the greatest EMV.

Uses the $\chi^2$ test to see if there is any significant difference in preferences.

The human resources department of a large finance company is attempting to determine if an employee’s performance is influenced by their undergraduate degree subject. Personnel ratings are used to judge performance and the task is to use expected frequencies and the chi-squared statistic to test the null hypothesis that there is no association.

Find out whether the data presented in this question follows a Poisson distribution. Uses the $\chi^2$ test.

One-way ANOVA example

Solving an equation of the form $ax \equiv\;b\;\textrm{mod}\;n$  where $\operatorname{gcd}(a,n)|r$. In this case we can find all solutions. The user is asked for the two greatest.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Exercise using a given uniform distribution $Y$, calculating the expectation and variance as well as asking for the CDF. Also finding  $P( b \lt Y \lt c)$ for given values of $b,\;c$.

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.

Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

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

Multiplication of $2 \times 2$ matrices.

Very elementary matrix multiplication. 

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

A box contains $n$ balls, $m$ of these are red the rest white.

$r$ are drawn without replacement.

What is the probability that at least one of the $r$ is red?

Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.

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

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$. Find least integer $N$ s.t.  $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Normal distribution $X \sim  N(\mu,\sigma^2)$ given. Find $P(a \lt X \lt b)$. Find expectation, variance, $P(c \lt \overline{X} \lt d)$ for sample mean $\overline{X}$.

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find  $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.