149 results for "distribution".

Question in Clodagh's workspace
rebelmaths
Application of the binomial distribution given probabilities of success of an event.
Finding probabilities using the binomial distribution.

Question in Julie's workspace
Application of the Poisson distribution given expected number of events per interval.
Finding probabilities using the Poisson distribution.
rebelmaths

Question in STAT7008
Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Question in STAT7008
Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Question in STAT7008
Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Question in Stats
No description given

Question in STAT7008
rebelmaths
Printing errors in the work produced by a particular film occur randomly at an average rate of p per page.
i.What is the probability that a one page document will contain x1 printing error(s)?
ii.If a n page document is printed, calculate the probability of having more than x2 errors. Assume a Poisson distribution. 
Question in Content created by Newcastle University
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 $\mu$.

Question in Content created by Newcastle University
Arrivals given by exponential distribution, parameter $\theta$ and $Y$, sample mean on interarrival times. Find and calculate unbiased estimator for $\theta$.

Question in Content created by Newcastle University
Looking up ttables.

Question in Content created by Newcastle University
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.

Question in Content created by Newcastle University
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 $\lambda$.

Question in Content created by Newcastle University
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 $\lambda$.

Question in Content created by Newcastle University
For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the tstatistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Question in Content created by Newcastle University
Given 3 observations from a $\operatorname{Poisson}(\mu)$ distribution find the likelihood, the log likelihood and the MLE for $\mu$.

Question in Content created by Newcastle University
Given descriptions of 3 random variables, decide whether or not each is from a Poisson or Binomial distribution.

Question in Content created by Newcastle University
Find out whether the data presented in this question follows a Poisson distribution. Uses the $\chi^2$ test.

Question in Content created by Newcastle University
Application of the Poisson distribution given expected number of events per interval.
Finding probabilities using the Poisson distribution.

Question in Content created by Newcastle University
Application of the binomial distribution given probabilities of success of an event.
Finding probabilities using the binomial distribution.

Question in Content created by Newcastle University
Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Question in Content created by Newcastle University
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 $b,\;c$.

Question in Content created by Newcastle University
Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

Question in Content created by Newcastle University
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 $\displaystyle \operatorname{E}[X]=\int_{\infty}^{\infty}xf_X(x)\;dx$.

Question in Content created by Newcastle University
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 $\overline{X}$.

Question in Content created by Newcastle University
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 $a,\;b,\;c$.

Question in Content created by Newcastle University
Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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

Question in Content created by Newcastle University
Given the parameters of a bivariate Normal distribution $(X,Y)$ find the parameters of the Normal Distributions: $aX,\;bY,\;cX+dY,\; Y(X=f),\;X(Y=g)$

Question in Content created by Newcastle University
$f(x,y)$ 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 $P(Y \le bX \ge c)$

Question in Content created by Newcastle University
Given a normal distribution $X \sim N(m,\sigma^2)$ find $P(X \lt a),\; a \lt m$ and the conditional probability $P(X \gt b  X \gt c)$ where $b \lt m$ and $c \gt m$.