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

Simple probability question. Counting number of occurences of an event in a sample space with given size and finding the probability of the event.

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

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

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 $a,\;b,\;c$.

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

Example showing how to calculate the probability of A or B using the law $p(A \;\textrm{or}\; B)=p(A)+p(B)-p(A\;\textrm{and}\;B)$. 

Also converting percentages to probabilities.

Easily adapted to other applications.

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Calculate definite integrals: $\int_0^\infty\;e^{-ax}\,dx$, $\int_1^2\;\frac{1}{x^{b}}\,dx$, $\; \int_0^{\pi}\;\cos\left(\frac{x}{2n}\right)\,dx$

Given constant demand for a product, calculate the economic order quantity, and the minimum cost per year.

Given constant demand for a product, with a single break point on the price, calculate the economic order quantity, and the minimum cost per year.

Calculating simple probabilities using the exponential distribution.

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

$W \sim \operatorname{Geometric}(p)$. Find $P(W=a)$, $P(b \le W \le c)$, $E[W]$, $\operatorname{Var}(W)$.

$Y \sim \operatorname{Poisson}(p)$. Find $P(Y=a)$, $P(Y \gt b)$, $E[Y],\;\operatorname{Var}(Y)$.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 10 paired observations.

Spearman rank correlation calculated. 8 paired observations.

Calculate the principal value of a complex number.

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

Finding probabilities using the binomial distribution.

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

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.

Calculate outcomes for different configurations of rolling two dice. 

Calculate a speed in m/s given distance and time taken, then convert that to km/hour

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.

Calculate relative frequencies in a variety of scenarios.

The amount of money a person gets on their birthday follows an arithmetic sequence.

Calculate the amount on a given birthday, then calculate the sum up to that point.