DaniecIf sample size of 100 are selected from a population with a mean of 28 and a standard deviation of 18,what is the standard error of the mean

2022-04-02
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DaniecIf sample size of 100 are selected from a population with a mean of 28 and a standard deviation of 18,what is the standard error of the mean

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Answered 2022-04-21
Author has **137** answers

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asked 2022-04-18

How do you call this system?

Is there a specific name for a dynamical system that depends on the relative indexation $i\pm k$ for some k? For example, consider the following dynamical system defined on a ring of cells by

$\begin{array}{rl}{\dot{u}}_{i}& ={u}_{i}+2({v}_{i-1}+{v}_{i+1})\\ {\dot{v}}_{i}& ={u}_{i}-{v}_{i}\end{array}$

for each cell i, where the derivative is with respect to time t.

The main reason I ask this is because I won't to compare this kind of systems with systems involving spatial coordinates, u(x,t), as in reaction-diffusion equations.

asked 2022-04-08

I'm trying to determine the convergence of this series:

$\sum _{n=1}^{\infty}(\frac{{\displaystyle 1}}{{\displaystyle 2}}\xb7\frac{{\displaystyle 3}}{{\displaystyle 4}}\xb7\frac{{\displaystyle 5}}{{\displaystyle 6}}\xb7...\frac{{\displaystyle 2n-3}}{{\displaystyle 2n-2}}\xb7\frac{{\displaystyle 2n-1}}{{\displaystyle 2n}}{)}^{a}$

asked 2022-03-21

Find a polynomial f(x) of degree 3 that has the following zeros. 8 ( multiplicity 2), -4.

asked 2022-03-29

Find the values of b such that the function has the given maximum value.

Maximum value: 62

f(x) = −x2 + bx − 19

b = (smaller value)

b = (larger value)

asked 2022-04-05

Find a matrix such that the systems are equivalent

Take the system

$$\{\begin{array}{l}w={v}^{\prime}\\ {v}^{\u2033}-\mu {v}^{\prime}+v=0\end{array}$$

for $\mu \in \mathbb{R}$

Find a constant matrix $A}^{\mu$ such that the above system is equivalent to

$\left[\begin{array}{c}v\text{'}\\ w\text{'}\end{array}\right]={A}^{\mu}\left[\begin{array}{c}v\text{'}\\ w\text{'}\end{array}\right]$

My first thought was to find a solution to $v{}^{\u2033}-\mu {v}^{\prime}+v=0$. Taking the characteristic polynomial as ${r}^{2}-\mu r+1=0$, I get $r=\frac{1}{2}(\mu \pm \sqrt{{\mu}^{2}-4})$. Not really sure what to do at this point, however. Another way to solve this might be first to replace v' in the second equation with w to get $v{}^{\u2033}-\mu w+v=0$ but I'm not sure where to go from there either.

asked 2022-03-04

Consider the IVP

{ y' = 2y

{y(0) = 1

a) Find the exact solution of the IVP

b) Using step ℎ = 0.2, find an approximate solution of the PVI at point = 1.0

b1) Euler's method

b2) Improved Euler Method

b3) Fourth-order Runge-Kutta method

c) Compare the approximate solutions obtained in the previous items with the exact solution.

asked 2022-03-18

a) Consider the following functional relation, f, defined as:

$f:R\to R,f\left(x\right)={x}^{2}$

Determine whether or not fis a bijection. If it is, prove it. If it is not, show why it is not

b) Consider the set

$F=\{y\mid y=a{x}^{3}+b\}$

a, b being constants such that $a\ne 0$ and $x\in R$.

Is $F=R$? If so, prove it. If not, explain in details why it is not the case.