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24 results.

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.
General scalar multiplication (same as WBQ 1.10)
Ready to use
Question in Linear Algebra 1st year by Julia Goedecke

Simple scalar multiplication of a general vector with the important scalars 0, 1, -1. Just the variable name is randomised.
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 $X$ .
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 $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .
BS1.1
Draft
Question in Bill's workspace by Bill Foster

Choosing whether given random variables are qualitiative or quantitative.
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
Log-likelihood and maximum likelihood estimator for PDF
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$ .
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 CBA0_4
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$ .
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 $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$ .
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 $\overline{X}$ .
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 $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .
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?
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.
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 $P(Y=a)$ , $P(Y \gt b)$ , $E[Y],\;\operatorname{Var}(Y)$ .
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 $P(X \ge c)$ .
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, 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 $P(X=a)$ , $P(X \leq b)$ , $E[X],\;\operatorname{Var}(X)$ .
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 $P(X \lt a)$ .
Determine if variables are qualitative or quantitative
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Choosing whether given random variables are qualitiative or quantitative.
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 $P(a \lt X \lt b)$ .
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 $P(X \lt a)$ .
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 $P(a \lt X \lt b)$ .

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