Em importante estudo sobre a economia brasileira na década de 1960, Simonsen defende que a política antiinflacionária adotada pelo PAEG apresentou a seguinte característica:

Item 0 - era uma política gradualista de combate à inflação e assemelhava-se, neste aspecto, à proposta, embora não implementada, do Plano Trienal do Governo Goulart;

Julgue a afirmativa:

Item 2 - Se u, v e w são vetores linearmente independentes, então v+w, u+w e u+v são também linearmente independentes;

Suponha que X e Y sejam variáveis aleatórias independentes, com distribuições de Bernoulli com parâmetros p e q, isto é,

!$ X = { \begin{cases} 1\,\,com\,probabilidade\,\,\,\,p\\0\,\,\,com\,probabilidade\,\,\,1-p \end{cases}} !$

e

!$ Y = { \begin{cases} 1\,\,com\,probabilidade\,\,\,\,q\\0\,\,\,com\,probabilidade\,\,\,1-p \end{cases}} !$

Defina Z = aY + bX, para a e b constantes.

E[ ] e V[ ] representam, respectivamente, expectativa e variância. Julgue a afirmativa abaixo:

Item 3 - Se b=0, Z e X são independentes;

Considere as informações contidas na tabela a seguir, sobre um país hipotético, para os anos de 2006 a 2008. Assuma que sejam produzidos apenas 2 bens finais, chamados X e Y. O preço de cada bem é expresso em unidades monetárias ($). A unidade de medida de cada variável está entre parênteses. Com base nas informações da tabela, julgue as afirmativas a seguir:

Obs.: Para o cálculo do PIB real, não utilize encadeamento.

Item 4- A taxa de crescimento anual do PIB real per capita independe da escolha do ano-base para os preços.

Julgue a afirmação abaixo de acordo com o modelo de equilíbrio geral com trocas simples:

Item 1 - Em um sistema de equilíbrio geral de trocas simples, são determinados os preços relativos e absolutos;

Seja !$ \Phi (x,y) = xy !$ a função real definida no quadrante !$ A = \left \{ (x,y) | x ge 0\,e\,y \ge 0 \right \} !$

Julgue o item abaixo:

Item 3 - O valor mínimo do problema de otimização min_A 4x + 9y, sujeito a condição !$ \Phi ( x,y)=1 !$, é igual a 1/12;

Text 2

Excerpts from:

Peek-a-boo

Astronomers get some new toys to play
with

FEW scientists believe that the space shuttle has helped their profession. Mostly, it has been used to convey astronauts to a space station that has produced little worthwhile research and to launch satellites that might have been put into orbit more cheaply by old-fashioned, throwaway rockets. But it has done one thing to assist astronomers. It has allowed what is probably their most famous instrument to be repaired and upgraded. That instrument is the Hubble space telescope, which took the picture of the Carina nebula shown above, and has snapped more than half a million other images over the years. Now, as the shuttle programme draws to its close (the final launch will take place next year), Hubble is to be given its last makeover by the crew of Atlantis. On top of that, if the week has gone well, two other satellites intended to probe the universe’s earliest days will have been launched.

The mission to Hubble, which began on May 11th and is planned to last 11 days, will install a wide-field camera that will let the telescope see galaxies previously beyond its reach. Using this, the eager coteries of astronomers who have access to the instrument will be able to observe young, hot stars that glow mainly in the ultraviolet part of the spectrum. They will also be able to see the first stars and galaxies that formed in the universe, which are now so old and distant that their light has been relegated to the infra-red part of the spectrum by the “red shift” caused by the universe’s expansion. These wonders can be observed only from space, because ozone and water in the Earth’s atmosphere absorb light at those wavelengths.

(...)

(From The Economist print edition, May 14^th 2009)

According to the text, the mission to Hubble

Item 1 - will remove a camera;

Text 2

Excerpts from:

Peek-a-boo

Astronomers get some new toys to play
with

FEW scientists believe that the space shuttle has helped their profession. Mostly, it has been used to convey astronauts to a space station that has produced little worthwhile research and to launch satellites that might have been put into orbit more cheaply by old-fashioned, throwaway rockets. But it has done one thing to assist astronomers. It has allowed what is probably their most famous instrument to be repaired and upgraded. That instrument is the Hubble space telescope, which took the picture of the Carina nebula shown above, and has snapped more than half a million other images over the years. Now, as the shuttle programme draws to its close (the final launch will take place next year), Hubble is to be given its last makeover by the crew of Atlantis. On top of that, if the week has gone well, two other satellites intended to probe the universe’s earliest days will have been launched.

The mission to Hubble, which began on May 11th and is planned to last 11 days, will install a wide-field camera that will let the telescope see galaxies previously beyond its reach. Using this, the eager coteries of astronomers who have access to the instrument will be able to observe young, hot stars that glow mainly in the ultraviolet part of the spectrum. They will also be able to see the first stars and galaxies that formed in the universe, which are now so old and distant that their light has been relegated to the infra-red part of the spectrum by the “red shift” caused by the universe’s expansion. These wonders can be observed only from space, because ozone and water in the Earth’s atmosphere absorb light at those wavelengths.

(...)

(From The Economist print edition, May 14^th 2009)

We can infer from the text that

Item 0 - the majority of scientists agree that the space shuttle has been useful to them;

Sobre a recuperação da economia brasileira na década de 1930 é correto afirmar:

Item 2 - A política de descentralização federativa posterior à “Revolução de 1930” permitiu que os estados defendessem, por meio de políticas próprias, o preço dos produtos de exportação;

Avalie a afirmação abaixo:

Item 1 - Suponha que uma carteira de ativos arriscados possui retorno esperado !$ r^e = 21 \% !$ e variância !$ \sigma^2= 0,09 !$. O ativo sem risco oferece um retorno !$ r^f = 3 \% !$. Então, de acordo com o modelo média-variância, o preço do risco da carteira é p = 2;