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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 $X$.

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

Finding probabilities using the Poisson distribution.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

The data is fitted by linear and quadratic regression.  First, find a linear regression equation for the $n$ data points, $20 \le n \le 35$.

They then are shown that the quadratic regression is often a better fit as measured by SSE. Also users can experiment with fitting polynomials of higher degree.

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

Finding probabilities using the binomial distribution.

Find a regression equation.

Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

Also includes an updated SSE to see how the sum of the squares of the residuals varies with the regression line.

Find a regression equation.

Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

Also includes an updated SSE to see how the sum of the squares of the residuals varies with the regression line.

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

Finding probabilities using the binomial distribution.

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

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

Finding probabilities using the Poisson distribution.

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 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. 

Given sample data find mean, standard deviation, median, interquartile range.

Note that there are different versions of the upper and lower quartiles, so you may want to include your own versions - see the user defined functions in the question.

Find a regression equation.

Given vectors  $\boldsymbol{A,\;B}$, find the angle between them.

Given vectors $\boldsymbol{A}$ and $\boldsymbol{B}$, find their inner product.

Determine if various combinations of vectors are defined or not.

When are vectors $\boldsymbol{A,\;B}$ perpendicular?

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

rebelmaths

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

When are vectors $\boldsymbol{v,\;w}$ orthogonal?

Part b) is not answered in Advice, the given solution is for a different question.

Determine if various combinations of vectors are defined or not.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.