Search - Content created by Newcastle University

294 results in Content created by Newcastle University - search across all projects.

Perform t-test given sample mean and standard deviation
Draft
Question by Newcastle University Mathematics and Statistics

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.
Multiply 2x2, 2x1 and 1x2 matrices
Draft
Question by Newcastle University Mathematics and Statistics

Very elementary matrix multiplication.
Multiply 2x2 matrices
Draft
Question by Newcastle University Mathematics and Statistics

Multiplication of $2 \times 2$ matrices.
Multiple and partial correlation(old)
Draft
Question by Newcastle University Mathematics and Statistics

Multiple correlation question. Given the correlation coefficent of $Y$ with $X_1$ is $r_{01}$ , the correlation coefficent of $Y$ with $X_2$ is $r_{02}$ and the correlation coefficent of $X_1$ with $X_2$ is $r_{12}$ then explain the proportion of variablity of $Y$ . Also find the partial corr coeff between $Y$ and $X_2$ after fitting $X_1$ and find how much of the remaining variability in $Y$ is explained by $X_2$ after fitting $X_1$ .
Finding limits by substitution,
Draft
Question by Newcastle University Mathematics and Statistics

Using simple substitution to find $\lim_{x \to a} bx+c$ , $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$ .
Find expected profit of gambles,
Draft
Question by Newcastle University Mathematics and Statistics

Given a large number of gambles, find the expected profit.
Find expectation, variance and probability sample mean in range for normal distribution, ,
Draft
Question by Newcastle University Mathematics and Statistics

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 $\overline{X}$ .
Find eigenvalues, characteristic polynomial and a normalised eigenvector of a 3x3 matrix
Draft
Question by Newcastle University Mathematics and Statistics

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$ .
Find eigenvalues and eigenvectors of matrices, and power of one matrix
Draft
Question by Newcastle University Mathematics and Statistics

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$ .
Find limit of a sequence
Draft
Question by Newcastle University Mathematics and Statistics

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$ . Find $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$ .
Find limits of sequences
Draft
Question by Newcastle University Mathematics and Statistics

Seven standard elementary limits of sequences.
Determine if vectors form a spanning set
Draft
Question by Newcastle University Mathematics and Statistics

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.
Determine limit of fractional power sequence
Draft
Question by Newcastle University Mathematics and Statistics

Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$ . Find least integer $N$ s.t. $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$
Invert a 3x3 matrix using row operations
Draft
Question by Newcastle University Mathematics and Statistics

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$ .
Find quartiles, range and interquartile range of a small sample, ,
Draft
Question by Newcastle University Mathematics and Statistics

Given 32 datapoints in a table find their minimum, lower quartile, median, upper quartile, and maximum.
Convert gambling odds to probabilities, ,
Draft
Question by Newcastle University Mathematics and Statistics

Converting odds to probabilities.
Calculate probabilities from a normal distribution,
Draft
Question by Newcastle University Mathematics and Statistics

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$ .
Mathematics and statistics for bioinformatics
Draft
Exam (19 questions) by Newcastle University Mathematics and Statistics

Questions used in a university course titled "Mathematics and statistics for bioinformatics"
Maclaurin and Taylor series
Draft
Exam (2 questions) by Newcastle University Mathematics and Statistics

Find the first few terms of the Maclaurin and Taylor series of given functions.
Linear programming
Draft
Exam (2 questions) by Newcastle University Mathematics and Statistics

Solve a linear programming problem, and perform sensitivity analysis.
Linear algebra
Draft
Exam (15 questions) by Newcastle University Mathematics and Statistics

Questions used in a university course titled "Linear algebra"
Maclaurin series (three terms)
Draft
Question by Newcastle University Mathematics and Statistics

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
Do three given vectors form a spanning set and are they linearly independent?
Draft
Question by Newcastle University Mathematics and Statistics

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$ .
Limits of sequences
Draft
Exam (8 questions) by Newcastle University Mathematics and Statistics

Questions about the limits of sequences from a first year pure maths course.
Indefinite integral by substitution
Draft
Question by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Integral of improper polynomial fraction
Draft
Question by Newcastle University Mathematics and Statistics

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$ . Enter the constant of integration as $C$ .
Integration: Indefinite integral
Draft
Question by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Indefinite integral of improper polynomial fraction
Draft
Question by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{nx^3+mx^2+nx + p}{1+x^2}\;dx$ . Solution involves $\arctan$ .
Indefinite integral by substitution
Draft
Question by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Indefinite integral of polynomial fraction
Draft
Question by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{nx^3+mx^2+px +m}{x^2+1} \;dx$

Content created by Newcastle University

Show results for Show results for

Refine by Refine by

Status

Author

Tags

Usage rights

Ability Level

Topics