Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.

Instructions on dealing with functions in Numbas.

Given a codeword in $w=\mathbb{Z}^4_3$ find and list all codewords at Hamming distance $1$ from $w$.

A simultaneous equations question with integers only

Simple trig equations with degrees

Simple trig equations with radians

Trigonometric equations with degrees

Trigonometric equations with radians

More difficult trigonometric equations with degrees

More difficult trigonometric equations with radians

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More work with dividing and multiplying algebraic fractions

Practice with fractions

Straightforward solving linear equations question.

Straightforward solving linear equations question

Straightforward solving linear equations question

Straightforward solving linear equations question

A simultaneous equations question with integers only

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $0$ and $2 \pi$ and careful with quadrants!

Find the general solution of $y''+2py'+(p^2-q^2)y=A\sin(fx)$ in the form  $A_1e^{ax}+B_1e^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral. Use initial conditions to find $A_1,B_1$.

Given that $\displaystyle \int^i_j x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)\ln(cx)\; dx $

Split $\displaystyle \frac{b}{(cx + d)(px+q)}$ into partial fractions.

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.

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