162 results for "calculations".

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• Exam (5 questions)

You are allowed 38 minutes to complete this test.

You may use rough paper for your calculations.

• Exam (5 questions)

You are allowed 31 minutes to complete this test.

You may use rough paper for your calculations.

• Question

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

• Question

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

• Question

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

• Question

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

• Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

• Question

Double integrals (2) with numerical limits

• Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

• Find the unit vector parallel to a given vector.

Interim calculations in Advice should be presented in enough accuracy to ensure that the final calculations are to 3dps.

• Question

Four questions on finding least upper bounds and greatest lower bounds of various sets.

• Question

Two factor ANOVA example

• Question

Given sum of sample from a Normal distribution with unknown mean $\mu$ and known variance $\sigma^2$. Find MLE of $\mu$ and one of four functions of $\mu$.

• Question

Using a random sample from a population with given mean and variance, find the expectation and variance of three estimators of $\mu$. Unbiased, efficient?

• Question

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$.

• Question

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.

• Question

Given data on probabilities of three levels of success of three options and projections of the profits that the options will accrue depending on the level of success, find the expected monetary value (EMV) for each option and choose the one with the greatest EMV.

• Question

Calculations in $\mathbb{Z_n}$ for three values of $n$.

• Question

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

• Question

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

• Question

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

• Question

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

• Question

Multiplication of $2 \times 2$ matrices.

• Question

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

• Question

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

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

• Question

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 $\overline{X}$.

• Question

Seven standard elementary limits of sequences.

• Question

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

• Question

$x_n=\frac{an+b}{cn+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \le 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$.