Newton's Method Solving an Equation February 10

What would be the Newton's method in the form $x_{k+1}=g(x_k)$ to solve the equation $$f(x)=x^bx+b^2-d^2=0$$ in which both $b>0,d>0$ are parameters? Additionally, I need to show that $|g'(x)|\le 1/2$ whenever $|x-b|\ge d/\sqrt{2}$ and also that $

complete the proof for this statement February 10    3

$$\forall x \in \mathbb{R}, x \neq 0 \implies \frac{1}{x^2\:+3}\:<\:\frac{4}{5}\: $$I thought of doing the contrapositive but not sure what to do next. $$ \frac{1}{x^{2\:}+3}\:\ge \frac{4}{5}$$$$\implies 0\ge 4x^2\:+7 $$Because $x^2+3 > 0$ for every

Proving that a statement about $ February 10    3

I need to do assignment for my homework, in which I need to prove that the following statement is valid. $$ (s<t \text{ and } t<u)\implies(s<u) $$I need to do this assignment using the laws and definitions of inequality.The problem is that I don'

Asymptotic standard normal distribution February 10    1

Asymptotic standard normal distribution
I need to solve the following exercise.Assume that $X_\lambda$ is Poisson distributed with mean $\lambda$ . Show that $Y(\lambda) = \frac{X_\lambda - \lambda}{\sqrt{\lambda}}$ is asymptotic ...

Sum of 'inverse' Normal (1/X) random variables. Equivalent resistance calculation February 10    2

Sum of 'inverse' Normal (1/X) random variables. Equivalent resistance calculation
Consider the case of $N$ resistances $R$ connected in parallel. The equivalent resistance of such a circuit is calculated as follows$$ \frac{1}{R_{eq}} = \underbrace{\frac{1}{R} + \frac{1}{R ...

definition of a sufficient statistic February 10    1

The "normal" definition of a sufficient statistics is via independence of the pdf (conditional on the statistic) of the parameter $\theta$. The Fisher-Neyman theorem gives a nice characterization:The statistic $T$ is sufficient iff $f(x;\theta)

On the computation of the Hessian matrix. February 10

On the computation of the Hessian matrix.
I'm trying to compute the Hessian matrix of a data fit of an ODE model to some data. Below is a cut out of the instructions I'm following (which can also be found at Gutenkunst, R.N., Waterf ...

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