Nt1310 Unit 1

Words: 287

Pages: 2

Open Document

\section{Preliminaries}
Lemma $2.1$ in Cai and Wang (2016) has provided a formula to determine the first derivative for the function $g(c)=E[ D((X-c)_{+})]$, where $D$ is a convex and nondecreasing function defined on $\R^{+}$.
\begin{lemma}(Lemma 2.1 Cai and Wang (2016))\label{3-lm1}
Let $g(c)=E[\xi D((X-c)_{+})]$, where $\xi$ is a non-negative random variable. $D$ is a convex and increasing function defined on $\R^{+}$. Assume $g(c)c\}}],$$
$$g'_{-}(c)=-E[\xi D'_{+}((X-c)_{+})I_{\{X\geq c\}}],$$ and both of them are finite. If $D$ is differentiable with $D'(0)=0$, then
$$g'(c)=-E[\xi D'((X-c)_{+})].$$
\end{lemma}

\noindent Lemma $2.2$ in Cai and Wang (2016) introduced a result about the well-known conclusion about the minimizers of convex program with no constraints according to Rockafellar (2011).
\begin{lemma}(Lemma 2.2 Cai and Wang …show more content…
In addition, the objective function defined in \eqref{3-eq01} satisfies $g\geq 0$, $h\geq 0$, $0 c\}}], \\
E[g(X)\varphi_{1+}^{'}((I(X)-c)_{+})I_{\{I(X)\geq c\}}]&\geq E[h(X)\varphi_{2-}^{'}(X-I(X)+c)],
\end{aligned}
\right.
\end{equation}
where $\varphi_{i-}^{'}$ and $\varphi_{i+}^{'}$ represent the corresponding left and right derivatives of $\varphi_{i}$, $i=1,2$. If $\varphi_{1}$ and $\varphi_{2}$ are strictly convex, the solution is unique. If $\varphi_{1}$ and $\varphi_{2}$ are differentiable and $\varphi'_{1}(0)=\varphi'_{2}(0)=0$, the optimal reinsurance premium principles $c^{*}_{X,I,g,h}$ are solutions to
\begin{equation}\label{3-eq2}
E[h(X)\varphi_{2}^{'}(X-I(X)+c)]= E[g(X)\varphi_{1}^{'}((I(X)-c)_{+})].
\end{equation}
\end{theorem}

\begin{proof}
Similar as Proposition 3.1 (a) in Cai and Wang (2016), we can get that $f_{1}(c)$ is finite, non-negative, convex, and satisfies

Nt1310 Unit 1

a) Before the Action Users 1. Avoid open cables such as wire cuts on the power adapter. 2. Disconnect the Uninterruptible Power Supply (UPS) from the socket. 3. Ensure the PC is off. 4. Keep water away from the PC or any other liquid. 5. Ensure no child is around to play with the system before the action. 6. All equipment connecting to the PC should be put on an elevated position. 7. The main power supply should remain switched off. 8. Analyze past response plans on the same that have been conducted…

Words 1105 - Pages 5

Nt1310 Unit 1

1. The United States Congress authorized the establishment of a Medical service on 27 July 1775. The establishment of this Medical Service enabled the Army to obtain the budget to buy adequate amount of medicine, equipment, and build medical facilities to treat Soldiers. As the enemy and type of casualties keep changing, today, the Medical Service is able to quickly prepare for any war because there is money available to buy any new equipment to prevent and treat soldiers. This move help strengthened…

Words 584 - Pages 3

Nt1310 Unit 1

MEDIA REPORT ANALYSIS 1. Identify the areas of law that are relevant to the chosen media report, and explain how they are relevant to the matters outlined in the report. Based on the article ‘Double Trouble’ (Pownall and Brown, 2014), the number of childcare centers in Western Australia that has breaking rules and unable to secure and monitored the children has increase rapidly as twice compare to last year. Tort law According to the article there are so many evidences regarding to negligence…

Words 1182 - Pages 5

Nt1310 Unit 1

mode supports upto four different users simultaneously. But this is possible only on the downlink [1] [3] [4]. Figure 2 explains the pictorially explains the concept of MU-MIMO using 4 antennas. V.…

Words 518 - Pages 3

Nt1310 Unit 1

tools, and structures of content areas or academic disciplines 5c: Using their own knowledge, appropriate early learning standards, and other resources to design, implement, and evaluate meaningful, challenging curricula for each child Artifact 1 1- Title of the Artifact - Melting Ice Activity 2- Description of Artifact: What is it? For what class was it developed? What was the purpose of the assignment? This artifact has been developed in ECED 304-Integrating Learning Standards in Early…

Words 1170 - Pages 5

Nt1310 Unit 1

UNIT OVERVIEW Unit 1 Arranging Close Study Focus Creation Discipline High School Ensembles: Music Unit Focus Students apply their knowledge of a song and style to create a new arrangement for a chamber ensemble (4‐6 musicians). The arrangements will apply melodies to various voices and creatively address accompaniment parts through variations in rhythms, harmonies, and countermelodies. Essential Questions - What does it mean to be an arranger? - What is the difference between a verse and chorus…

Words 821 - Pages 4

Nt1310 Unit 1

1. What is the difference between a. and a. What did you learn from this project? Throughout the course of this project, I was really pleased with how much I learned about the regulatory surveillance process. It was a relatively new world for me, and it was very interesting to see what happened. surveillance looks like for such a large entity as UPMC. I also think it prompted me to learn and think about tailoring information to certain audiences in a different way. I have learned in previous courses…

Words 1068 - Pages 5

Nt1310 Unit 1

This system, designed to streamline operations within the computer laboratory environment, incorporates key features including equipment tracking, security protocols, and inventory management. By providing administrators with comprehensive insights into usage trends, the system facilitates resource efficiency and informed decision-making. A primary focus is placed on addressing the challenge of balancing student access to learning technology with maintaining a productive classroom environment. The…

Words 1132 - Pages 5

Nt1310 Unit 1

Task 1 Explain how computer networks work A network is a collection of computers, servers, mainframes, network devices, peripherals or any other devices connected to one another that allow you to share data amongst each other. An example could be internet- which connects millions of people all over the world. One of the first Computer networks to use were packet switching, ARPANET it was devolved in the mid 60’s and was considered to be the direct predecessor of the modern internet. I will…

Words 4887 - Pages 20

Nt1310 Unit 1 Exercise 1

1. Oscilloscope: The display of the waveform on the oscilloscope gives immediate qualitative information on the degree and type of distortion. Sometimes cases of resonances are individual through the observable distortion that is present in the voltage and current waveforms. 2. Spectrum Analyzers: These instruments display the power distribution of a signal as a function of frequency. A certain range of frequencies is scanned, and all the components, harmonics, and interharmonics of the analyzed…

Words 315 - Pages 2