Newcastle University Mathematics and Statistics

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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.

Deciding whether or not  three sampling methods are simple random sampling, stratified sampling, systematic or judgemental sampling. Also whether or not the method of selection is random, quasi-random or non-random.

Approximating integral of a linear function 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.

Approximating integral of a linear function 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 random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

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

Find a regression equation.

Given sample data find mean, standard deviation, median, interquartile range,

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.

Find a regression equation.

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.

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.

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

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e $ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$.

For example: $((q \lor \neg p) \to (p \land \neg q)) \lor \neg q$