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29 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.
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.
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 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.
BS3.4
Draft
Question in Bill's workspace by Bill Foster

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .
BS3.2
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.
BS3.3
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.
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.
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
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 $\mu$ .
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?
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 $\theta$ .
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 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 $b,\;c$ .
Find expectation, variance and probability sample mean in range for normal distribution, ,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Normal distribution $X \sim N(\mu,\sigma^2)$ given. Find $P(a \lt X \lt b)$ . Find expectation, variance, $P(c \lt \overline{X} \lt d)$ for sample mean $\overline{X}$ .
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 $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .
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 $a,\;b,\;c$ .
Calculate probability, CDF, expected value and variance of binomial distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$X \sim \operatorname{Binomial}(n,p)$ . Find $P(X=a)$ , $P(X \leq b)$ , $E[X],\;\operatorname{Var}(X)$ .
Calculate probability, expected value and variance of a geometric distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$W \sim \operatorname{Geometric}(p)$ . Find $P(W=a)$ , $P(b \le W \le c)$ , $E[W]$ , $\operatorname{Var}(W)$ .
Calculate probability, expected value and variance of a Poisson distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$Y \sim \operatorname{Poisson}(p)$ . Find $P(Y=a)$ , $P(Y \gt b)$ , $E[Y],\;\operatorname{Var}(Y)$ .
Find parameters of normal distributions from bivariate distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given the parameters of a bivariate Normal distribution $(X,Y)$ find the parameters of the Normal Distributions: $aX,\;bY,\;cX+dY,\; Y|(X=f),\;X|(Y=g)$
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.
Bivariate continuous distribution - marginals and conditional probability,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$f(x,y)$ is the PDF of a bivariate distribution $(X,Y)$ on a given rectangular region in $\mathbb{R}^2$ . Write down the limits of the integrations needed to find $P(X \ge a)$ , the marginal distributions $f_X(x),\;f_Y(y)$ and the conditional probability $P(Y \le b|X \ge c)$
Calculate probabilities from binomial distribution
Draft
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.

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