Content created by Newcastle University

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

Looking up t-tables. 

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

Multiple response question (2 correct out of 4) covering properties of Riemann integration. Selection of questions from a pool.

Modular arithmetic

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.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.

Given a piecewise CDF $F_X(b)$ which is discontinuous at several points, find the probabilities at those points and also find the value of $F_X(b)$ at a continuous point and the expectation.

This cdf is a step function and is therefore the cdf of a discrete random variable. This should be stated somewhere in the statement or the solution. Apart from this the question is correct.

Friedman test, 5 subjects, 4 treatments.

Questions on right-angled triangles asking for the calculation of angles using inverse-trigonometrical functions.

Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.

Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct,  but the feedback indicates that the third was wrong.

Multiple response question (2 correct out of 4) covering properties of continuity and limits of functions. Selection of questions from a pool.

Given a payoff table with two states and five actions, identify which actions are admissible, then the maximax, maximin, and minimax regret actions.

Should state that input is by integers or fractions. Also  the maximax, maximin and minimax regret actions are not asked for.

Transform a second order ODE into 2D non-autonomous and 3D autonomous dynamical systems of ODEs.

Transform a second order ODE into 2D non-autonomous and 3D autonomous dynamical systems of ODEs.

Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient.

Finding the distance between two complex numbers using the modulus of their difference. Three parts.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.