21 results authored by Alex Van den Hof  search across all users.

Question in Alex's workspace
There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

Question in LeicesterPhysPractice
Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.

Question in LeicesterPhysPractice
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 $\displaystyle \operatorname{E}[X]=\int_{\infty}^{\infty}xf_X(x)\;dx$.

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

Question in LeicesterPhysPractice
Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$

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

Question in LeicesterPhysPractice
Given the pdf $f(x)=\frac{abx}{c},\;r \leq x \leq s,\;f(x)=0$ else, find $P(X \gt p)$, $P(X \gt q  X \gt t)$.

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

Question in LeicesterPhysPractice
Application of the Poisson distribution given expected number of events per interval.
Finding probabilities using the Poisson distribution.
rebelmaths

Question in LeicesterPhysPractice
Elementary Exercises in multiplying matrices.

Question in LeicesterPhysPractice
$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Question in LeicesterPhysPractice
Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Question in LeicesterPhysPractice
Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Question in LeicesterPhysPractice
aij notation and definition of the order of a matrix.

Question in Simon's workspace
$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Question in Simon's workspace
aij notation and definition of the order of a matrix.

Question in Simon's workspace
Elementary Exercises in multiplying matrices.

Question in Simon's workspace
Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Question in Simon's workspace
Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Question in Simon's workspace
Multiplying two 2 x 2 matrices.

Question in Simon's workspace
Multiplication of $2 \times 2$ matrices.