For any vectors u, v and w, show that the vectors u+v, u+w and v+w form a linearly dependent set.

2022-04-06

For any vectors u, v and w, show that the vectors u+v, u+w and v+w form a linearly dependent set.

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asked 2022-05-05

Suppose$U=\{(x,y,x+y,x-y,2x)\in {F}^{5},x,y\in F\}$ . Find a subspace $W$of ${F}^{5}$ such that ${F}^{5}=U\oplus W$.

asked 2022-04-18

1.)In a maths test, there are 10 mcq with 4 possiable answers and 15 true false questions. In how many ways can the 25 question be answered?

2) Let, A be set of workers and B. be set of Job. Let R1 be relation from A to B (a,b) is in [we assume be a binary relation from A B such that R₁. If worker 'A' is assign to job B. that worker might be assign to same Job] Let R2 be a binary relation on A such that (b1, b2) is in R2. It b1, b2 can get along each other if a they are assign to same job. State condition in terms of R₁, R2 and (possiably binary relation derived from R1 and R2 Such that assignment of worker in the job according to R1 will not took of worker that can't get along with one another on the same job.

asked 2022-05-18

asked 2022-04-04

Find a 95 confidence interval for $\theta$ based on inverting the test statistic statistic $\hat{\theta}$.

For our data we have ${Y}_{i}\sim N(\theta {x}_{i},1){\textstyle \phantom{\rule{1em}{0ex}}}\text{for}{\textstyle \phantom{\rule{1em}{0ex}}}i=1,\dots ,n.$

Therefore it can be proven that the MLE for $\theta$ is given by

$\hat{\theta}=\frac{\sum {x}_{i}{Y}_{i}}{\sum {x}_{i}^{2}}$

To find the confidence interval I should invert the test statistic $\hat{\theta}$.

The most powerful unbiased size $\alpha =0,05$ test for testing

$H}_{0}:\mu ={\mu}_{0}{\textstyle \phantom{\rule{1em}{0ex}}}\text{vs.}{\textstyle \phantom{\rule{1em}{0ex}}}{H}_{1}:\mu \ne {\mu}_{0$

where ${X}_{1},\dots ,{X}_{n}\sim \text{}\text{iid}\text{}n(\mu ,{\sigma}^{2})$ has acceptance region

$A\left({\mu}_{0}\right)=\left\{\mathbf{x}:|\overline{x}-{\mu}_{0}|\le 1,96\sigma /\sqrt{n}\right\}.$

Substituting my problem (I think) we get that the most powerful unbiased size $\alpha =0,05$ test for testing

$H}_{0}:\theta =\hat{\theta}{\textstyle \phantom{\rule{1em}{0ex}}}\text{vs.}{\textstyle \phantom{\rule{1em}{0ex}}}{H}_{1}:\theta \ne \hat{\theta$

has acceptance region $\{A\left(\hat{\theta}\right)=\{\mathbf{y}:|\stackrel{\u2015}{y}-\hat{\theta}|\le 1,\frac{96}{\sqrt{n}}\}$

or equivalently, $A\left(\hat{\theta}\right)=\left\{\mathbf{y}:\frac{\sqrt{n}\overline{y}-1,96}{\sqrt{n}{x}_{i}}\le \hat{\theta}\le \frac{\sqrt{n}\overline{y}+1,96}{\sqrt{n}{x}_{i}}\right\}$

Substituting $\hat{\theta}=\sum {x}_{i}Y\frac{i}{\sum}{x}_{i}^{2}$ we obtain

$A\left(\hat{\theta}\right)=\left\{\mathbf{y}:\frac{\sqrt{n}\overline{y}-1,96}{\sqrt{n}{x}_{i}}\le \frac{\Sigma {x}_{i}Yi}{\Sigma {x}_{i}^{2}}\le \frac{\sqrt{n}\overline{y}+1,96}{\sqrt{n}{x}_{i}}\right\}$

This means that my $1-0,05=0,95\left(95\mathrm{\%}\right)$ confindence interval is defined to be

$C\left(y\right)=\{\hat{\theta}:y\in A\left(\hat{\theta}\right)\}$

But I can't seem to find anything concrete and I feel that I've made mistakes somewhere. What to do?

asked 2022-04-09

**Solve the initial value problem**

asked 2022-03-29

Find a vector function that represents the curve of intersection of the two surfaces of the cylinder x^2+y^2=4 and the surface z=xy.

asked 2022-04-15

Find the exponential model that fits the points shown in the table. (Round the exponent to four decimal places.)

x | 0 | 5 |
---|---|---|

y | 3 | 1 |