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

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Two numbers from a set of $5$ numbers are chosen at random, without replacement. Find the distribution $X$ of their sum and $E[X]$.

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 $P(a \lt X \lt b)$.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

A comparison of the mean of two groups.

A comparison of the mean of two groups.

A comparison of the mean of two groups.

A comparison of the mean of two groups.

A comparison of the means of three groups.

A comparison of the means of three groups.

A comparison of the means of four groups.