• 1.

  Ready to use
  An experiment is performed twice, each with $5$ outcomes $x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.
• 2.

  draft
  Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.
• 3.

  draft
  Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.
• 4.

  draft
  Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.
• 5.

  Ready to use
  Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..
• 6.

  Ready to use
  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.
• 7.

  draft
  Converting odds to probabilities.
• 8.

  Ready to use
  Rolling a pair of dice. Find probability that at least one die shows a given number.
• 9.

  Doesn't work
  A box contains $n$ balls, $m$ of these are red the rest white. $r$ are drawn without replacement. What is the probability that at least one of the $r$ is red?
• 10.

  Ready to use
  Two numbers are drawn at random without replacement from the numbers m to n. Find the probability that both are odd given their sum is even.
• 11.

  Ready to use
  Given subset $T \subset S$ of $m$ objects in $n$ find the probability of choosing without replacement $r\lt n-m$ from $S$ and not choosing any element in $T$.
• 12.

  Ready to use
  Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.
• 13.

  draft
  Given a large number of gambles, find the expected profit.
• 14.

  draft
  Determine if the following describes a probability mass function. $P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.
• 15.

  Ready to use
  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 $a,\;b,\;c$.
• 16.

  draft
  Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.
• 17.

  draft
  Calculating simple probabilities using the exponential distribution.
• 18.

  Ready to use
  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?
• 19.

  draft
  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 $\overline{X}$.

There are no questions in this group.