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25 results.

SA1 Types of data
Ready to use
Question in Skills Audits for Maths and Stats by Lauren Desoysa and 3 others

Decide whether each of the described sets of data is drawn from a discrete or continuous distribution.
Normal distribution probability and percentiles,
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Given normal distribution $\operatorname{N}(m,\sigma^2)$ find $P(a \lt X \lt b),\; a \lt m,\;b \gt m$ and also find the value of $X$ corresponding to a given percentile $p$ %.
BS3.4
Draft
Question in Bill's workspace by Bill Foster

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .
BS3.5
Draft
Question in Bill's workspace by Bill Foster

Exercise using a given uniform distribution $X$ , calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$ .
BS3.6
Draft
Question in Bill's workspace by Bill Foster

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.
Prove discontinuity of a function at a given point
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.
True/false statements about continuity at a point
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

No description given
True/false statements about Riemann integration,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple response question (2 correct out of 4) covering properties of Riemann integration. Selection of questions from a pool.
Find expectation, variance and CDF of uniform distribution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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 $b,\;c$ .
Construct a probability distribution function, then find CDF and expectation
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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 $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$ .
Calculate probabilities from a normal distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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 expectation, variance and CDF of uniform distribution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Exercise using a given uniform distribution $Y$ , calculating the expectation and variance as well as asking for the CDF. Also finding $P(Y \le a)$ and $P( b \lt Y \lt c)$ for a given values $a,\;b,\;c$ .
Use piecewise CDF to find probabilities at given points, and the expectation.
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

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.
Construct PDF and find CDF,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The random variable $X$ has a PDF which involves a parameter $k$ . Find the value of $k$ . Find the distribution function $F_X(x)$ and $P(X \lt a)$ .
PDF and CDF of continuous uniform random variable,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$X$ is a continuous uniform random variable defined on $[a,\;b]$ . Find the PDF and CDF of $X$ and find $P(X \ge c)$ .
Find CDF of given exponential distribution, and expectation and variance,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$
Calculate probabilities using the exponential distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Calculating simple probabilities using the exponential distribution.
True/false statements about continuity and differentiability,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

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.
True/false statements about properties of continuity and limits,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Multiple response question (2 correct out of 4) covering properties of continuity and limits of functions. Selection of questions from a pool.
Discrete and continuous data
Ready to use
Question in Transition to university by Stanislav Duris and 1 other

Deicde whether each of the described sets of data is drawn from a discrete or continuous distribution.
Ricardo's copy of IS2.2
Ready to use
Question in Ricardo's workspace by Ricardo Monge

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 $P(a \lt X \lt b)$ .
Max and Min 6
Ready to use
Question in Bill's workspace by Bill Foster

$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$ . Are there stationary points and local maxima, minima? Has $g$ a global max, global min?
Katie's copy of Max and Min 6
Ready to use
Question in Katie's workspace by Katie Dexter

$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$ . Are there stationary points and local maxima, minima? Has $g$ a global max, global min?
IS2.2
Ready to use
Question in Bill's workspace by Bill Foster

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 $P(a \lt X \lt b)$ .
IS2.1
Ready to use
Question in Bill's workspace by Bill Foster

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

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