Find p (x>7)

Ryza L. Dela Cruz
2022-07-26

Find p (x>7)

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asked 2021-01-31

The centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and Questions Navigation Menu preliminary estimate of the proportion who smoke of .26.

a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02?(to the nearest whole number) Use 95% confidence.

b) Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c) What is the 95% confidence interval for the proportion of smokers in the population?(to 4 decimals)?

a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02?(to the nearest whole number) Use 95% confidence.

b) Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c) What is the 95% confidence interval for the proportion of smokers in the population?(to 4 decimals)?

asked 2022-11-08

I am a student of Pure Mathematics and also interested in programming .I have learnt C++,SAGE .

Recently I have started learning "Cryptography" .But there are many definitions involved here like polynomial time algorithm,time complexity etc.

My question is it all right for a student in Pure Mathematics to study Cryptography or as time progresses I will eventually fall out of place and lose interest in this subject.

Is Cryptography more suitable for computer science graduates or it does not matter which background a student is from to study this?

Please share your thoughts here as i am still in my early days and may help to change the subject if necessary before it is too late

Recently I have started learning "Cryptography" .But there are many definitions involved here like polynomial time algorithm,time complexity etc.

My question is it all right for a student in Pure Mathematics to study Cryptography or as time progresses I will eventually fall out of place and lose interest in this subject.

Is Cryptography more suitable for computer science graduates or it does not matter which background a student is from to study this?

Please share your thoughts here as i am still in my early days and may help to change the subject if necessary before it is too late

asked 2022-09-19

Euclid's view and Klein's view of Geometry and Associativity in Group

One common item in the have a look at of Euclidean geometry (Euclid's view) is "congruence" relation- specifically ""congruence of triangles"". We recognize that this congruence relation is an equivalence relation

Every triangle is congruent to itself

If triangle ${T}_{1}$is congruent to triangle ${T}_{2}$then ${T}_{2}$is congruent to ${T}_{1}$.

If ${T}_{1}$is congruent to ${T}_{2}$and ${T}_{2}$is congruent to ${T}_{3}$, then ${T}_{1}$is congruent to ${T}_{3}$.

This congruence relation (from Euclid's view) can be translated right into a relation coming from "organizations". allow $Iso({\mathbb{R}}^{2})$ denote the set of all isometries of Euclidean plan (=distance maintaining maps from plane to itself). Then the above family members may be understood from Klein's view as:

∃ an identity element in $Iso({\mathbb{R}}^{2})$ which takes every triangle to itself.

If $g\in Iso({\mathbb{R}}^{2})$ is an element taking triangle ${T}_{1}$to ${T}_{2}$, then ${g}^{-1}\in Iso({\mathbb{R}}^{2})$ which takes ${T}_{2}$to ${T}_{1}$.

If $g\in Iso({\mathbb{R}}^{2})$ takes ${T}_{1}$to ${T}_{2}$and $g\in Iso({\mathbb{R}}^{2})$ takes ${T}_{2}$ to ${T}_{3}$ then $hg\in Iso({\mathbb{R}}^{2})$ which takes ${T}_{1}$ to ${T}_{3}$.

One can see that in Klein's view, three axioms in the definition of group appear. But in the definition of "Group" there is "associativity", which is not needed in above formulation of Euclids view to Kleins view of grometry.

Question: What is the reason of introducing associativity in the definition of group? If we look geometry from Klein's view, does "associativity" of group puts restriction on geometry?

One common item in the have a look at of Euclidean geometry (Euclid's view) is "congruence" relation- specifically ""congruence of triangles"". We recognize that this congruence relation is an equivalence relation

Every triangle is congruent to itself

If triangle ${T}_{1}$is congruent to triangle ${T}_{2}$then ${T}_{2}$is congruent to ${T}_{1}$.

If ${T}_{1}$is congruent to ${T}_{2}$and ${T}_{2}$is congruent to ${T}_{3}$, then ${T}_{1}$is congruent to ${T}_{3}$.

This congruence relation (from Euclid's view) can be translated right into a relation coming from "organizations". allow $Iso({\mathbb{R}}^{2})$ denote the set of all isometries of Euclidean plan (=distance maintaining maps from plane to itself). Then the above family members may be understood from Klein's view as:

∃ an identity element in $Iso({\mathbb{R}}^{2})$ which takes every triangle to itself.

If $g\in Iso({\mathbb{R}}^{2})$ is an element taking triangle ${T}_{1}$to ${T}_{2}$, then ${g}^{-1}\in Iso({\mathbb{R}}^{2})$ which takes ${T}_{2}$to ${T}_{1}$.

If $g\in Iso({\mathbb{R}}^{2})$ takes ${T}_{1}$to ${T}_{2}$and $g\in Iso({\mathbb{R}}^{2})$ takes ${T}_{2}$ to ${T}_{3}$ then $hg\in Iso({\mathbb{R}}^{2})$ which takes ${T}_{1}$ to ${T}_{3}$.

One can see that in Klein's view, three axioms in the definition of group appear. But in the definition of "Group" there is "associativity", which is not needed in above formulation of Euclids view to Kleins view of grometry.

Question: What is the reason of introducing associativity in the definition of group? If we look geometry from Klein's view, does "associativity" of group puts restriction on geometry?

asked 2022-09-04

Finding the optimal strategy

You have a deck of 32 playing cards. Somebody draws one card after another and shows them to you. At any point of time you may bet that the next card is black. If it is indeed black you earn $10, otherwise nothing. If you don't do anything you earn nothing as well. Find the optimal strategy.

In other words you should find the point of time where the quota of remaining red cards in the deck is maximal.

You have a deck of 32 playing cards. Somebody draws one card after another and shows them to you. At any point of time you may bet that the next card is black. If it is indeed black you earn $10, otherwise nothing. If you don't do anything you earn nothing as well. Find the optimal strategy.

In other words you should find the point of time where the quota of remaining red cards in the deck is maximal.

asked 2022-10-12

I am carrying out a category on discrete arithmetic and i'm inquisitive about skipping my faculties transition courses so that you can take a rigorous theory path next semester (topology, analysis, abstract algebra). What are a few properly transition books for me to examine that provide troubles and a few solutions so i will monitor my development, as well as being very , almost laboriously, particular in every step of evidence such as theorem packages. as an instance, i have observed abbots expertise analysis to be pretty cogent but Laczkovich Conjecture and evidence to be lacking some data important for me to understand some proofs as much as I would love. thank you for any assist

asked 2022-09-02

Numerical method for steady-state solution to viscous Burgers' equation

I am reading a paper in which a specific partial differential equation (PDE) on the space-time domain $[-1,1]\times [0,\mathrm{\infty})$ is studied. The authors are interested in the steady-state solution. They design a finite difference method (FDM) for the PDE. As usual, there are certain discretizations in time-space, ${U}_{j}^{n}$, that approximate the solution u at the mesh points, $u({x}_{j},{t}_{n})$. The authors conduct the FDM method on $[-1,1]\times [0,T]$, for T sufficiently large such that

$\left|\frac{{U}_{j}^{N}-{U}_{j}^{N-1}}{\mathrm{\Delta}t}\right|<{10}^{-12},\phantom{\rule{1em}{0ex}}\mathrm{\forall}j,$

where ${t}_{N}=T$ is the last point in the time mesh and $\mathrm{\Delta}t$ is the distance between the points in the time mesh. The approximations for the steady-state solution are given by $\{{U}_{j}^{N}{\}}_{j}$

I wonder why the authors rely on the PDE to study the steady-state solution. As far as I know, the steady-state solution comes from equating the derivatives with respect to time to 0 in the PDE. The remaining equation is thus an ordinary differential equation (ODE) in space. To approximate the steady-state solution, one just needs to design a FDM for this ODE, which is easier than dealing with the PDE for sure. Is there anything I am not understanding properly?

For completeness, I am referring to the paper Supersensitivity due to uncertain boundary conditions. The authors deal with the PDE ${u}_{t}+u{u}_{x}=\nu {u}_{xx}$, $x\in (-1,1)$, $u(-1,t)=1+\delta $, $u(1,t)=-1$, where $\nu ,\delta >0$ . They employ a FDM for this PDE for large times until the steady-state is reached. Why not considering the ODE$u{u}^{\prime}=\nu {u}^{\u2033}$, $u(1)=-1$, $u(1)=-1$, instead?

I am reading a paper in which a specific partial differential equation (PDE) on the space-time domain $[-1,1]\times [0,\mathrm{\infty})$ is studied. The authors are interested in the steady-state solution. They design a finite difference method (FDM) for the PDE. As usual, there are certain discretizations in time-space, ${U}_{j}^{n}$, that approximate the solution u at the mesh points, $u({x}_{j},{t}_{n})$. The authors conduct the FDM method on $[-1,1]\times [0,T]$, for T sufficiently large such that

$\left|\frac{{U}_{j}^{N}-{U}_{j}^{N-1}}{\mathrm{\Delta}t}\right|<{10}^{-12},\phantom{\rule{1em}{0ex}}\mathrm{\forall}j,$

where ${t}_{N}=T$ is the last point in the time mesh and $\mathrm{\Delta}t$ is the distance between the points in the time mesh. The approximations for the steady-state solution are given by $\{{U}_{j}^{N}{\}}_{j}$

I wonder why the authors rely on the PDE to study the steady-state solution. As far as I know, the steady-state solution comes from equating the derivatives with respect to time to 0 in the PDE. The remaining equation is thus an ordinary differential equation (ODE) in space. To approximate the steady-state solution, one just needs to design a FDM for this ODE, which is easier than dealing with the PDE for sure. Is there anything I am not understanding properly?

For completeness, I am referring to the paper Supersensitivity due to uncertain boundary conditions. The authors deal with the PDE ${u}_{t}+u{u}_{x}=\nu {u}_{xx}$, $x\in (-1,1)$, $u(-1,t)=1+\delta $, $u(1,t)=-1$, where $\nu ,\delta >0$ . They employ a FDM for this PDE for large times until the steady-state is reached. Why not considering the ODE$u{u}^{\prime}=\nu {u}^{\u2033}$, $u(1)=-1$, $u(1)=-1$, instead?

asked 2022-11-19

How to deal with lack of peers?

I am pursuing a B.S in Mathematics(freshman) in a country where people rarely study math for the sake of it and in a new university with good professors. Yet, it is new and I suffer from the lack of peers and it is literally impossible to pick up mathematical conversations on ideas with students . As a result, I find it difficult to exchange ideas with others.

Is there something which can be done to make sure that lack of peers or the pressure to push oneself doesn't harm me much?

I am pursuing a B.S in Mathematics(freshman) in a country where people rarely study math for the sake of it and in a new university with good professors. Yet, it is new and I suffer from the lack of peers and it is literally impossible to pick up mathematical conversations on ideas with students . As a result, I find it difficult to exchange ideas with others.

Is there something which can be done to make sure that lack of peers or the pressure to push oneself doesn't harm me much?