É correta a afirmativa:

Item 1 - Suponha que !$ X_1, X_2, ..., X_n !$ sejam variáveis aleatórias independentes e identicamente distribuídas, com distribuição uniforme no intervalo [0,1]. Seja !$ \sum^n_{i=1}X_i/n !$. Pelo Teorema Central do Limite, à medida que !$ n \rightarrow \infty , \sqrt{n}((\overline{X}-1/2)/\sqrt{1/12}) !$ aproxima-se de uma distribuição normal padrão.

Julgue a afirmativa:

Item 4 - Seja !$ \sum_{n=1}^\infty a_n !$ uma série convergente e !$ \varphi : N \rightarrow N !$ uma bijeção qualquer. Se !$ b_n=a_{\varphi(n)} !$, então !$ \sum_{n=1}^\infty b_n=\sum_{n=1}^\infty a_n !$.

Com relação às escolhas ótimas dos consumidores, constata-se que:

Item 4 - Nas funções demandas geradas a partir de uma função utilidade do tipo U(X,Y) = X2+ Y2as demandas individuais por cada bem são independentes do preço do outro.

Julgue a afirmativa:

Seja !$ f:R^* \rightarrow R\ !$, tal que !$ x^2f(x)=x~^2+7x+3 !$. Julgue a afirmativa:

Item 4 - !$ \lim_{x \rightarrow \infty}f(x)+\lim_{x \rightarrow \infty}\dfrac{ln(2+e^x)}{3x}=\dfrac{4}{3} !$.

Seja !$ A=(a_{ij}) !$ a uma matriz !$ n \times n !$ com entradas !$ a_{ij} \in R\ !$. Julgue a afirmativa:

Item 4 - Suponha que !$ a_{ij}=0 !$ a quando !$ i + j !$ for par e !$ a_{ij}=1 !$ quando !$ i + j !$ for ímpar. Se !$ n \ge 3 !$, então !$ A !$ tem posto !$ n !$.

Charlemagne

Choosing new friends

The European Union is struggling to help Arab revolutionaries

Apr 7th 2011 | from the print edition

IN ITS desire to surround itself with a “ring of friends”, Europe never really asked if it was rubbing shoulders with the right sort of chums. From Algeria to Belarus, it has been encircled for the most part by police states. The Arab revolts are belatedly overturning old assumptions. Take France: the same Rafale fighter jets it tried to sell to Colonel Muammar Qaddafi are now being sent into action against him.

The European Union, too, is revising its “neighbourhood policy” in the hope that its claim to be promoting economic and political reformin return for greater integration with the EU will no longer seem such a mockery. For years European officials negotiated action plans with countries and wrote reports bemoaning their lack of democracy, yet kept paying autocrats billions of euros. Until recently the EU was negotiating “deep and comprehensive” free-trade agreements with just two neighbours: Ukraine, even though it has been backsliding on civil liberties, and Libya.

Europe’s neighbourhood policy is a sort of enlargement-lite. It offers countries on the EU’s rim the prospect of integration short of full membership—“everything but institutions” went the early slogan. It was born from a wish to reassure Ukraine that it would not be cut off after the admission of eight ex-communist states (plus Malta and Cyprus) to the EU in 2004. But it was soon expanded to include other new neighbours (Belarus and Moldova), older Mediterranean neighbours and, for good measure, the Caucasus (Armenia, Azerbaijan and Georgia).

It has not all been cynical. To the east, the reforming government of Moldova is being rewarded with generous aid. Meanwhile, the EU has frozen assets and restricted visas for Belarus’s leaders after they rigged elections and suppressed protests. But in the south the promotion of democracy and the rule of law has been a fiction. As one Eurocrat puts it, “they pretended to implement the human rights commitment. We pretended to open up our programmes and policies.”

Last month the European Commission rushed out a revised Mediterranean policy insisting it would not be “a passive spectator”. Next month it will publish a more comprehensive review, including eastern neighbours. For Stefan Fule, one of the commissioners in charge, the first paper tried to answer “the easy question”: how to help Tunisia and Egypt after they had got rid of their dictators. The second will try to answer the harder questions: what to do about countries that have liberalised only partly (eg, Morocco and Jordan) or hardly at all (eg, Syria and Algeria).

(...)

It is tempting to draw a parallel between the fall of the Berlin Wall in 1989 and the Arab spring of 2011. But one big difference is that the ex-communist countries had a burning wish to “return” to Europe. Arab neighbours have no such ambition. And eastern neighbours, though eligible in theory, know the EU is not ready to expand beyond the Balkans. Without the lure of membership, the EU struggles to find effective foreign-policy tools.

Where does Europe’s interest lie?

As with its past inability to shift Arab dictators, the EU will struggle to shape the outcome of the Arab spring. But it should try, not least because its actions in the south influence the east. The neighbourhood is where the EU has the greatest chance of having an impact. As a union, it may not have military power, but it has useful economic and political tools.

Some officials worry that the emphasis on promoting democracy will tie Europe’s hands. What if Arab countries do not democratise? What if the Arab spring turns to winter? Europe will still have interests to pursue in energy security, fighting terrorism, managing migration and more. Such concerns are legitimate. But the Arab spring highlights another vital interest. The old Arab allies are falling; given the stability the EU wants, democracy offers abetter hope of taking radical Islam.Policies should be better tailored for each neighbour. Europe cannot change geography, so it will have to deal with all the countries on its rim, democratic or autocratic. But in its circle of neighbours, it must always demonstrate that its best friends are the democrats.

from the print edition | Europe

In the text the writer says that:

Item 4 - Eastern neighbours are not eligible for membership of the EU.

Julgue a afirmativa:

Seja !$ f:R^* \rightarrow R\ !$, tal que !$ x^2f(x)=x~^2+7x+3 !$. Julgue a afirmativa:

Item 2 - !$ f !$ é decrescente em !$ (-\infty, 0) !$.

10Um trabalhador pode realizar dois níveis de esforço quando contratado por uma fábrica, alto ou baixo. A probabilidade de ocorrerem erros de produção é condicional ao nível de esforço do trabalhador. Se o trabalhador realiza o esforço alto a probabilidade de erro é 0,25 e se o trabalhador realiza o esforço baixo a probabilidade de erro se eleva para 0,75. A função de utilidade do trabalhador é dada por: !$ U(w,e)=100-\dfrac{10}{w}-e !$, em que !$ w !$ é o salário do trabalhador e e o nível de esforço, que assume o valor !$ e=2 !$, no caso do trabalhador realizar o esforço alto, e e=0no caso do trabalhador realizar esforço baixo. A única oportunidade de trabalho existente no mercado é dada por este posto na fábrica. O valor do produto depende de seu estado, ou seja, se o produto estiver perfeito o fabricante consegue vendê-lo a R$ 20,00 a unidade e se o produto apresentar algum defeito, devido aos erros de produção, o produto não é vendido e, portanto, seu valor é zero. Sabendo que o fabricante é neutro ao risco e maximiza o lucro esperado conhecendo as restrições do trabalhador, assinale falso ou verdadeiro:

Item 2 - Caso o fabricante queira que o trabalhador realize o esforço baixo deverá pagar salários distintos para cada estado da natureza, mas inferiores ao contrato proposto no caso de induzir o esforço alto.