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51 results.

Poisson (sales)
Ready to use
Question in Julie's workspace by Julie Crowley and 2 others

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

rebelmaths
Clodagh's copy of BS3.3 Binomial Cookies
Draft
Question in Clodagh's workspace by Clodagh Carroll and 1 other

rebelmaths

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.
MSS - Normal Distribution Area Mid
Ready to use
Question in MESH by Brent Le Cornu and 3 others

Students are asked to move an x-axis slider representing standard deviation on a normal distribution to make the area between (mean - slider value) and (mean + slider value) equal to a certain percentage. The 3 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.
MSS - Normal Distribution Area Left
Ready to use
Question in MESH by Brent Le Cornu and 1 other

Students are asked to move an x-axis slider on a normal distribution to make the area to the left of the slider equal to a certain percentage. The 6 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.
MSS - Normal Distribution Mean
Ready to use
Question in MESH by Brent Le Cornu and 1 other

Students are shown a normal distribution, and a slider that moves the distribution horizontally. They are asked to move it so that the mean is equal to a particular value.
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 $p$ %.
BS3.1
Draft
Question in Bill's workspace by Bill Foster and 1 other

Given descriptions of 3 random variables, decide whether or not each is from a Poisson or Binomial distribution.
Probability mass function of string of heads from weighted coin,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$ .
Calculate expectation and probabilities from Poisson distribution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.
Calculate expectation and a probability from a frequency table, , ,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$ , find the expectation $E$ and $P(X \gt E)$ .
Calculate probabilities from a binomial distribution
Needs to be tested
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.
BS3.2
Draft
Question in Bill's workspace by Bill Foster

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.
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 $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .
BS3.6
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.
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 $a$ .
BS3.3
Draft
Question in Bill's workspace by Bill Foster

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.
Binomial (practice of formula)
Ready to use
Question in Julie's workspace by Julie Crowley and 1 other

$X \sim \operatorname{Binomial}(n,p)$ . Find $P(X=a)$ , $P(X \leq b)$ , $E[X],\;\operatorname{Var}(X)$ .

rebelmaths
Probability sample mean is within d of the population mean
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given data on population mean and population standard deviation and three sampling sizes, calculate the probabilities that the sample means are within a specified distance from the population mean.
Find maximum likelihood estimator of mean of normal distribution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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 $\mu$ .
Unbiased estimator for exponential distribution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Arrivals given by exponential distribution, parameter $\theta$ and $Y$ , sample mean on inter-arrival times. Find and calculate unbiased estimator for $\theta$ .
2012 2013 CBA4_3
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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.
2012 2013 CBA3_3
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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 $\lambda$ .
2012 2013 CBA3_2
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

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 $\lambda$ .
2012 2013 CBA3_1
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

For a sample of size n from a normal distribution and given the mean of the sample and the standard deviation of the distribution, find the MLE for the mean. Also the expected information and a confidence interval for the mean.
20122013 CBA1_1
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given 3 observations from a $\operatorname{Poisson}(\mu)$ distribution find the likelihood, the log likelihood and the MLE for $\mu$ .
Find the expectation and variance of three estimators of the mean
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Using a random sample from a population with given mean and variance, find the expectation and variance of three estimators of $\mu$ . Unbiased, efficient?
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 $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$ .
Expectation and variance of combinations of estimators
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given three linear combinations of four i.i.d. variables, find the expectation and variance of these estimators of the mean $\mu$ . Which are unbiased and efficient?
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 $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .

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