For a sample of size n from a Poisson distribution $\operatorname{Poisson}(\lambda)$ and given the mean of the sample, find the MLE for $\lambda$. Also find the expected information and a confidence interval for $\lambda$.

For a sample of size n from an Exponential distribution $\operatorname{Exponential}(\lambda)$  and given the mean of the sample, find the MLE for $\lambda$. Also find the expected information and a confidence interval for $\lambda$.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Given a linear combination $Y$ of three independent random variables with given means and variances, find the mean of variance of $Y$.

Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.

Given 3 observations from a $\operatorname{Poisson}(\mu)$ distribution find the likelihood, the log likelihood and the MLE for $\mu$.

Looking up t-tables. 

Given sum of sample from a Normal distribution with unknown mean $\mu$ and known variance $\sigma^2$. Find MLE of $\mu$ and one of four functions of $\mu$.

Using a random sample from a population with given mean and variance, find the expectation and variance of three estimators of $\mu$. Unbiased, efficient?

Entering numbers in Numbas, Part 1.

Details on inputting numbers into Numbas.

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$. 

Looking up t-tables. 

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

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.

Enumerate the elements in some sets defined using set builder notation.

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Abstract simplex method question. Given optimal tableau, student must identify optimal solution and objective value.

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

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

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Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Given descriptions of  3 random variables, decide whether or not each is from a Poisson or Binomial distribution.

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

Simple probability question. Counting number of occurences of an event in a sample space with given size and finding the probability of the event.

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

Choosing whether given random variables are qualitative or quantitative.