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# Monte Carlo Simulation

If we have a random variable $H$, such that

$$H=B_1G_2\min(1,G_1)+B_2\frac{\min(2,G_1 G_2+G_2)}{n-B_1-B_2},$$ where $n$ is constant, $G_1$ and $G_2$ are independent lognormal with different parameters, $B_1\sim \operatorname{binom}(n,0.09)$, and $B_2\sim \operatorname{binom}(B_1, 0.02)$, so $B_1$ and $B_2$ are dependent.

It asks for the probability of H being larger than a constant number $c$, say $\operatorname{P}(H>c)$.

I know how to use Monte Carlo directly, but anyone could suggest a faster solution?

Thanks for your time!

-
What does "the probability that such thing that bigger" mean? – dfeuer Aug 16 '13 at 0:09
Sorry, just means Pr(H>c), but c can be choosen by any number. – Richard Li Aug 16 '13 at 1:32


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## Found 18 Documents (Results 1–18)

100
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### Extremal functions for a class of trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary. (English)Zbl 1478.46040

MSC:  46E35 58J05 58J32
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### The regularity lifting methods for nonnegative solutions of Lane-Emden system. (English)Zbl 1466.35214

MSC:  35J91 35J47 35B65
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### Asymptotic behaviors of solutions to a sixth-order Boussinesq equation with logarithmic nonlinearity. (English)Zbl 1466.35049

MSC:  35B40 35L35 35L76
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### On the uniqueness of solutions of a semilinear equation in an annulus. (English)Zbl 1471.35141

MSC:  35J61 35A02 35A24
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### A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations. (English)Zbl 1466.35168

MSC:  35J60 35B06
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### $$C^{2,\alpha}$$ estimates for solutions to almost linear elliptic equations. (English)Zbl 1471.35134

MSC:  35J60 35D40 35B45
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### Nonlinear Choquard equations with Hardy-Littlewood-Sobolev critical exponents. (English)Zbl 1466.35164

MSC:  35J60 35A01 35J20
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# DisappearinEbony

...

Flagged as Spam
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Featured By Owner Jul 26, 2007  Hobbyist Photographer
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# How do you find the polynomial function with roots 1, 7, and -3 of multiplicity 2?

Aug 10, 2015

$f \left(x\right) = 2 \left(x - 1\right) \left(x - 7\right) \left(x + 3\right) = 2 {x}^{3} - 5 {x}^{2} - 17 x + 21$

#### Explanation:

If the roots are 1,7,-3 then in factored form the polynomial function will be:

$f \left(x\right) = A \left(x - 1\right) \left(x - 7\right) \left(x + 3\right)$

Repeat the roots to get the required multiplicity:

$f \left(x\right) = \left(x - 1\right) \left(x - 7\right) \left(x + 3\right) \left(x - 1\right) \left(x - 7\right) \left(x + 3\right)$

Aug 11, 2015

The simplest polynomial with roots $1$, $7$ and $- 3$, each with multiplicity $2$ is:

$f \left(x\right) = {\left(x - 1\right)}^{2} {\left(x - 7\right)}^{2} {\left(x + 3\right)}^{2}$

$= {x}^{6} - 10 {x}^{5} - 9 {x}^{4} + 212 {x}^{3} + 79 {x}^{2} - 714 x + 441$

#### Explanation:

Any polynomial with these roots with at least these multiplicities will be a multiple of $f \left(x\right)$, where...

$f \left(x\right) = {\left(x - 1\right)}^{2} {\left(x - 7\right)}^{2} {\left(x + 3\right)}^{2}$

$= {\left({x}^{3} - 5 {x}^{2} - 17 x + 21\right)}^{2}$

$= {x}^{6} - 10 {x}^{5} - 9 {x}^{4} + 212 {x}^{3} + 79 {x}^{2} - 714 x + 441$

...at least I think I've multiplied this correctly.

Let's check $f \left(2\right)$ :

${2}^{6} - 10 \cdot {2}^{5} - 9 \cdot {2}^{4} + 212 \cdot {2}^{3} + 79 \cdot {2}^{2} - 714 \cdot 2 + 441$

$= 64 - 320 - 144 + 1696 + 316 - 1428 + 441 = 625$

${\left(\left(2 - 1\right) \left(2 - 7\right) \left(2 + 3\right)\right)}^{2} = {\left(1 \cdot - 5 \cdot 5\right)}^{2} = {\left(- 25\right)}^{2} = 625$


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# Integration of linear functions

## Homework Statement

If i integrate (2x+5) using the simplest rule, i get x2+5x+c, however if i use the linear function method, i would get (2x+5)^2/4 +c so simplifying it i get (4x^2+20x+25)/4 +c=x^2+5x+25/4+c. So does it mean when i use the two different methods my constant,c is different?

## Homework Equations

linear integration rule

## The Attempt at a Solution

So does it mean when i use the two different methods my constant,c is different?

Yes, there's no meaningful difference there.

thanks!

HallsofIvy
Homework Helper

## Homework Statement

If i integrate (2x+5) using the simplest rule, i get x2+5x+c, however if i use the linear function method, i would get (2x+5)^2/4 +c so simplifying it i get (4x^2+20x+25)/4 +c=x^2+5x+25/4+c. So does it mean when i use the two different methods my constant,c is different?

## Homework Equations

linear integration rule

## The Attempt at a Solution

So does it mean when i use the two different methods my constant,c is different?
C is an arbitrary constant. It doesn't matter whether you use "c" or "25/4+ c" it still represents some arbitrary constant.

Suppose you were given that dy/dx= 2x+ 5 and that y(0)= 1. Clearly y is the integral of 2x+ 5 so, integrating the first way, you would get y(x)= x2+ 5x+ c and then the addtional condition, that y(0)= 1, becomes y(0)= 02+ 5(0)+ c= c= 1 so you answer is y(x)= x2+ 5x+ 1.

Integrating the second way, y(x)= x2+ 5x+ 25/4+ c so that y(0)= 02+ 5(0)+ 25/4+ c= 25/4+ x= 1 so that c= 1- 25/4= -21/4. But that means that y(x)= x2+ 5x+ 25/4- 21/4= x2+ 5x+ 4/4= x2+ 5x+ 1 just as before.

Mentallic
Homework Helper

## Homework Statement

If i integrate (2x+5) using the simplest rule, i get x2+5x+c, however if i use the linear function method, i would get (2x+5)^2/4 +c so simplifying it i get (4x^2+20x+25)/4 +c=x^2+5x+25/4+c. So does it mean when i use the two different methods my constant,c is different?

## Homework Equations

linear integration rule

## The Attempt at a Solution

So does it mean when i use the two different methods my constant,c is different?

If I ever use a method of integration that gives me some constant such as +1 but then I also have a +c added on the end, I just merge them together to make it +c2 or +k or if the teacher isn't strict / doesn't care I'll just get rid of the 1.


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## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

We can find the force that the spring pushes when it is compressed 5.0 cm: $F = kx$ $F = (750~N/m)(0.050~m)$ $F = 37.5~N$ The spring pushes with a force of 37.5 N. According to Newton's third law, the athlete must also be pushing with a force of 37.5 N.


text: A.)What is the strength of the electric field at the position indicated by the dot in the figure? What is the direction of the electric field at the position indicated by the dot in the figure? B.)Specify the direction as an angle above the horizontal line.


text:
# Exercise 8-12 (Part Level Submission) Culver Company was formed on December 1, 2016. The following information...

###### Question:

Exercise 8-12 (Part Level Submission)

Culver Company was formed on December 1, 2016. The following information is available from Culver’s inventory records for Product BAP.
 Units Unit Cost January 1, 2017 (beginning inventory) 684 $6.00 Purchases: January 5, 2017 1,368 7.00 January 25, 2017 1,482 8.00 February 16, 2017 912 9.00 March 26, 2017 684 10.00 A physical inventory on March 31, 2017, shows 1,824 units on hand. (a)  Your answer is correct. Prepare schedule to compute the ending inventory at March 31, 2017, under FIFO inventory method.  CULVER COMPANY COMPUTATION OF INVENTORY FOR PRODUCT BAP UNDER FIFO INVENTORY METHOD March 31, 2017 Units Unit Cost Total Cost Beginning InventoryEnding InventoryPurchases January 5, 2017Purchases January 25, 2017Purchases February 16, 2017Purchases March 26, 2017$ $Beginning InventoryEnding InventoryPurchases January 5, 2017Purchases January 25, 2017Purchases February 16, 2017Purchases March 26, 2017 Beginning InventoryEnding InventoryPurchases January 5, 2017Purchases January 25, 2017Purchases February 16, 2017Purchases March 26, 2017 Beginning InventoryEnding InventoryPurchases January 5, 2017Purchases January 25, 2017Purchases February 16, 2017Purchases March 26, 2017$
 Attempts: 1 of 3 used

(b)

Prepare schedule to compute the ending inventory at March 31, 2017, under LIFO inventory method.
 CULVER COMPANY COMPUTATION OF INVENTORY FOR PRODUCT BAP UNDER LIFO INVENTORY METHOD March 31, 2017 Units Unit Cost Total Cost Beginning InventoryEnding InventoryPurchases January 5, 2017Purchases January 25, 2017Purchases February 16, 2017Purchases March 26, 2017  Beginning InventoryEnding InventoryPurchases January 5, 2017Purchases January 25, 2017Purchases February 16, 2017Purchases March 26, 2017 Beginning InventoryEnding InventoryPurchases January 5, 2017Purchases January 25, 2017Purchases February 16, 2017Purchases March 26, 2017 $## Answers #### Similar Solved Questions 1 answer ##### Exercise 6-10 Petty cash fund accounting LO P2 Palmona Co. establishes a$320 petty cash fund...
Exercise 6-10 Petty cash fund accounting LO P2 Palmona Co. establishes a $320 petty cash fund on January 1. On January 8, the fund shows$217 in cash along with receipts for the following expenditures: postage, $45; transportation-in,$11; delivery expenses, $13; and miscellaneous expenses,$34. Pal...
##### Smentfshowtest php?action-skipBiscorez? obile Homes Q https//quizletconv_ Homepre On last attempt;0 out of 1ore Inl gradebook L out of 1Next QuestonTr: another similar question reattempt last question below; Or select another questionFind the distance cotered by point moving With linear velocity for a time t if67 mihr andJ0 min2010~oleansttter j2 1 Duuioer (MkaEntei DXE for Doet Noi LrleGct HelpPounts possiblc This attempt Scere on last altempt: Scotecameboe
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##### Evaluate /sec'  tan" rdz+C
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##### Select the major product of the following reaction. + Mg/diethyl ether 1. 2.H20* Y YY YYY...
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man Company uses Departmental Overhead allocation to locate its manufacturing overhead costs. It has identified two departments: Miting and Finishing The Miling department locatie overhead sing machine hours, and the Finishing department totes overhead using labor hours. It has accumulated the follo...
##### 2. Differential equations and direction fields (a) Find the general solution to the differential equation y'...
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) ...
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##### Calculate the following integral rties of integrals 7/3 - dx d) z2 tan a da -1/3
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##### Point) In this exercise we consider finding the general solution of the first order linear equation y 3y = 0. This equation has an ordinary point at x and therefore has power series solution in the formWe learned how to easily solve problems Iike this in several different ways but here we want t0 consider the power series method:(1) Insert the formal power series into the differential equation and derive the recurrence [email protected] for n = [,2,NOTE that d is an arbitrary constant:Use the recurre
point) In this exercise we consider finding the general solution of the first order linear equation y 3y = 0. This equation has an ordinary point at x and therefore has power series solution in the form We learned how to easily solve problems Iike this in several different ways but here we want t0 c...
##### Short-run supply and long-run equilibrium, please and thank you Consider the competitive market for titanium. Assume...
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##### QUESTION NO: 02 (07 MARKS) CLO-[C3, Application) PLO-[ When Methane is burnet in the presence of oxygen it produces carbon dioxide and water; The equation for the reaction can be written as; CH,+0z L COz +HzO. Use the concept of applied linear = algebra to balance the given reaction equation:
QUESTION NO: 02 (07 MARKS) CLO-[C3, Application) PLO-[ When Methane is burnet in the presence of oxygen it produces carbon dioxide and water; The equation for the reaction can be written as; CH,+0z L COz +HzO. Use the concept of applied linear = algebra to balance the given reaction equation:...

-- 0.031352--


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# [Tugindia] Re: eaquation aligning

Ashis Kumar Mal akmal at ece.iitkgp.ernet.in
Sun Feb 19 06:42:38 CET 2006

On Sun, 19 Feb 2006 cdatta at vsnl.com wrote:
> i have used equationarray to align some equations. i am not sure if this is the same as the "eqnarry"(sic) that you mention. however, i am giving below a segment of the table code that i used in one of my notes.  remember to include in the preamble
> \usepackage{equationarray}
>
> \begin{eqnarray}
> E_{x} \,& = & - \quad { \frac{1} {k_{c}^{2} } }
>                     \left(
>                       j \omega \mu      { \frac {\partial H_{z}} {\partial y} } \, + \,
>                         \gamma          { \frac {\partial E_{z}} {\partial x} }
>                     \right) \\
> E_{y} \,& = &   \qquad { \frac{1} {k_{c}^{2} }}
>                     \left(
>                       j \omega \mu      { \frac {\partial H_{z}} {\partial x} } \, - \,
>                         \gamma          { \frac {\partial E_{z}} {\partial y} }
>                     \right) \\
> H_{x} \,& = &   \qquad { \frac{1} { k_{c}^{2}} }
>                     \left(
>                       j \omega \epsilon { \frac {\partial E_{z}} {\partial y} } \, - \,
>                         \gamma          { \frac {\partial H_{z}} {\partial x} }
>                     \right) \\
> H_{y} \,& = & - \quad  { \frac{1} { k_{c}^{2}} }
>                     \left(
>                       j \omega \epsilon { \frac {\partial E_{z}} {\partial x} } \, + \,
>                         \gamma          { \frac {\partial H_{z}} {\partial y} }
>                     \right)
> \end{eqnarray}
>
> you have also asked about a thesis format in latex.  i think there is a thesis class, namely thesis.cls.  you can search for that in ctan.
>
> let me know if the above helps.
> cheers.
> c.dattatreyan

Thanks a lot for a nice code. It worked but I would prefer to use "align"
for simplicity.

Regarding thesis, I am aware that such a class is there in CTAN /
other foreign universities etc. But I wanted to have a format which many
list users (especially who belongs to IIT/IISc) are using. It's very
difficult to chhose one from many.
And I'm surprised to note that many IIT's don't have a standard LaTeX
thesis format. And they are producing lots of PhD's written using LaTeX.

So, if someone belongs to IITX(!KGP) could supply me format it will be
highly appreciated.

Thanks again for your suggestions.

Best regards,
_Ashis
Kharagpur

More information about the tugindia mailing list


text:
Theory Manual Version 3.4
$\newcommand{\lyxlock}{}$
Subsubsection 7.1.8.1: Facet-To-Facet Sliding Up Subsection 7.1.8: Alternative Formulations Section 7.2: Biphasic Contact

#### 7.1.8.2 Sliding-Tension-Compression

The second alternative differs more significantly from the method described above. It also begins with the definition of a single contact integral over the slave surface. But a different derivation is followed to obtain the linearization of this contact integral. The main reason for this difference is a subtly alternative definition for the gap function. In this method, it is defined as follows. where, is the normal of the slave surface (opposed to the master normal as used in the derivation above). In this case, the point is no longer the closest point projection of onto the master surface, but instead is the normal projection along . The linearization of equation (7.1.8.2-2) now becomes, where, are the tangent vectors to the master surface at . Note that since is normal to the slave surface, equation (7.1.8.2-3) does not reduce to equation (7.1.2-7).
In one assumes frictionless contact, the contact traction can be written as follows, where, are the tangent vectors to evaluated at . Using (7.1.8.2-4) we can rewrite the contact integral as follows. where we assumed that the integration domain can be mapped to a 2D parametric domain, .
The linearization of (7.1.8.2-5) now proceeds in the usual fashion. Omitting the details, it can be shown that the linearization of the contact integral results in, where, and .
The discretization of the contact integral and its linearization now proceeds as usual. We will not derive the details, but it is important to point out that the resulting stiffness matrix for this particular contact formulation is not symmetric. Although this method has shown to give good results, especially in large compression problems, it was desirable to derive a symmetric version as well. Because of this, a slightly different formulation was also developed that does reduce to a symmetric stiffness matrix although this symmetric version did not seem to perform as well as the non-symmetric one.
Subsubsection 7.1.8.1: Facet-To-Facet Sliding Up Subsection 7.1.8: Alternative Formulations Section 7.2: Biphasic Contact


text:
[This article was first published on Quantargo Blog, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Make your first steps with the ggplot2 package to create a scatter plot. Use the grammar-of-graphics to map data set attributes to your plot and connect different layers using the + operator.

• Define a dataset for the plot using the ggplot() function
• Specify a geometric layer using the geom_point() function
• Map attributes from the dataset to plotting properties using the mapping parameter
• Connect different ggplot objects using the + operator
library(ggplot2)
ggplot(___) +
geom_point(
mapping = aes(x = ___, y = ___)
)

## Introduction to scatter plots

Scatter plots use points to visualize the relationship between two numeric variables. The position of each point represents the value of the variables on the x- and y-axis. Let’s see an example of a scatter plot to understand the relationship between the speed and the stopping distance of cars:

Each point represents a car. Each car starts to break at a speed given on the y-axis and travels the distance shown on the x-axis until full stop. If we take a look at all points in the plot, we can clearly see that it takes faster cars a longer distance until they are completely stopped.

## Quiz: Scatter Plot Facts

Which of the following statements about scatter plots are correct?
• Scatter plots visualize the relation of two numeric variables
• In a scatter plot we only interpret single points and never the relationship between the variables in general
• Scatter plots use points to visualize observations
• Scatter plots visualize the relation of categorical and numeric variables
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## Specifying a dataset

library(ggplot2)
ggplot(___) +
geom_point(
mapping = aes(x = ___, y = ___)
)

To create plots with ggplot2 you first need to load the package using library(ggplot2).

After the package has been loaded specify the dataset to be used as an argument of the ggplot() function. For example, to specify a plot using the cars dataset you can use:

library(ggplot2)
ggplot(cars)

Note that this command does not plot anything but a grey canvas yet. It just defines the dataset for the plot and creates an empty base on top of which we can add additional layers.

## Exercise: Specify the gapminder dataset

To start with a ggplot visualizing the gapminder dataset we need to:

1. Load the ggplot2 package
2. Load the gapminder package
3. Define the gapminder dataset to be used in the plot with the ggplot() function
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## Specifying a geometric layer

library(ggplot2)
ggplot(___) +
geom_point(
mapping = aes(x = ___, y = ___)
)

We can use ggplot’s geometric layers (or geoms) to define how we want to visualize our dataset. Geoms use geometric objects to visualize the variables of a dataset. The objects can have multiple forms like points, lines and bars and are specified through the corresponding functions geom_point(), geom_line() and geom_col():

## Quiz: Scatter Plot Layers

Which geometric layer should be used to create scatter plots in ggplot2?
• point_geom()
• geom()
• geom_scatter()
• geom_point()
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## Creating aesthetic mappings

library(ggplot2)
ggplot(___) +
geom_point(
mapping = aes(x = ___, y = ___)
)

ggplot2 uses the concept of aesthetics, which map dataset attributes to the visual features of the plot. Each geometric layer requires a different set of aesthetic mappings, e.g. the geom_point() function uses the aesthetics x and y to determine the x- and y-axis coordinates of the points to plot. The aesthetics are mapped within the aes() function to construct the final mappings.

To specify a layer of points which plots the variable speed on the x-axis and distance dist on the y-axis we can write:

geom_point(
mapping = aes(x=speed, y=dist)
)

The expression above constructs a geometric layer. However, this layer is currently not linked to a dataset and does not produce a plot. To link the layer with a ggplot object specifying the cars dataset we need to connect the ggplot(cars) object with the geom_point() layer using the + operator:

ggplot(cars) +
geom_point(
mapping = aes(x=speed, y=dist)
)

Through the linking ggplot() knows that the mapped speed and dist variables are taken from the cars dataset. geom_point() instructs ggplot to plot the mapped variables as points.

The required steps to create a scatter plot with ggplot can be summarized as follows:

1. Load the package ggplot2 using library(ggplot2).
2. Specify the dataset to be plotted using ggplot().
3. Use the + operator to add layers to the plot.
4. Add a geometric layer to define the shapes to be plotted. In case of scatter plots, use geom_point().
5. Map variables from the dataset to plotting properties through the mapping parameter in the geometric layer.

## Exercise: Visualize the “cars” dataset

Create a scatter plot using ggplot() and visualize the cars dataset with the car’s stopping distance dist on the x-axis and the speed of the car on the y-axis.

The ggplot2 package is already loaded. Follow these steps to create the plot:

1. Specify the dataset through the ggplot() function
2. Specify a geometric point layer with the geom_point() function
3. Map the speed to the x-axis and the dist to the y-axis with aes()
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## Exercise: Visualize the Gapminder dataset

Create a scatter plot using ggplot() and visualize the gapminder_2007 dataset with the GDP per capita gdpPercap on the x-axis and the life expectancy lifeExp of each country on the y-axis.

The ggplot2 package is already loaded. Follow these steps to create the plot:

1. Specify the gapminder_2007 dataset through the ggplot() function
2. Specify a geometric point layer with geom_point().
3. Map the gdpPercap to the x-axis and the lifeExp to the y-axis with aes()
Start Exercise

Create a scatter plot with ggplot is an excerpt from the course Introduction to R, which is available for free at quantargo.com

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