Julgue a seguinte alternativa:

Item 2 - No passeio aleatório com drift, y_t = c + y_t-1 + !$ \varepsilon_t !$, y₀ = 0, em que !$ \varepsilon_t !$ é um ruído branco com média zero e variância !$ \sigma^2 !$, a média de y_t varia com t.

Produto interno líquido a custo de fatores ..................................................................3.500

Formação bruta de capital fixo (do setor privado) .........................................................600

Variação de estoques (do setor privado) ........................................................................50

Impostos diretos ............................................................................................................350

Impostos indiretos .........................................................................................................150

Outras receitas correntes do governo (líquidas) .............................................................50

Consumo do governo ....................................................................................................350

Subsídios .......................................................................................................................100

Transferências ...............................................................................................................150

Depreciação ...................................................................................................................150

Déficit do balanço de pagamentos em transações correntes ........................................200

Com base nessas informações, julgue a seguinte alternativa:

Item 0 - O PIB a preços de mercado é igual a 3.900.

Seja !$ f \, : \, \mathbf{R}^2 \, \rightarrow \, \mathbf{R} !$ uma função diferenciável. Julgue a alternativa:

Item 1 - Se !$ H_f( \chi, \, y) \, = \, \begin {bmatrix} 3\chi^2 \,\,\, -1 \\ -1 \,\,\, 3y^2 \end {bmatrix} !$ é a matriz hessiana de !$ f !$ e !$ (0, \, 0) !$ é um ponto crítico de !$ f !$, podemos afirmar que !$ (0, \, 0) !$ é ponto de mínimo de !$ f !$.

Nos primeiros anos da década de 1960, a taxa de crescimento da economia brasileira passou por forte desaceleração, ao mesmo tempo em que a inflação crescia. Sobre este período pode-se afirmar:

Item 4 - O fim do período parlamentarista de Goulart, com o retorno ao presidencialismo em 1963, contribuiu para o abandono da política de estabilização, proposta no Plano Trienal, na primeira fase de seu governo.

Text 1

Excerpts from:

The “CSI effect”

Television dramas that rely on forensic science to solve crimes are affecting the administration of justice

Apr 22nd 2010 | From The Economist print edition

OPENING a new training centre in forensic science (...) at the University of Glamorgan in South Wales recently, Bernard Knight, formerly one of Britain’s chief pathologists, said that because of television crime dramas, jurors today expect more categorical proof than forensic science is capable of delivering. And when it comes to the gulf between reality and fiction, Dr Knight knows what he is talking about: besides 43 years’ experience of attending crime scenes, he has also written dozens of crime novels.

The upshot of this is that a new phrase has entered the criminological lexicon: the “CSI effect” after shows such as “CSI: Crime Scene Investigation”. In 2008 Monica Robbers, an American criminologist, defined it as “the phenomenon in which jurors hold unrealistic expectations of forensic evidence and investigation techniques, and have an increased interest in the discipline of forensic science.”

Now another American researcher has demonstrated that the “CSI effect” is indeed real. Evan Durnal of the University of Central Missouri’s Criminal Justice Department has collected evidence from a number of studies to show that exposure to television drama series that focus on forensic science has altered the American legal system in complex and far-reaching ways. His conclusions have just been published in Forensic Science International.

The most obvious symptom of the CSI effect is that jurors think they have a thorough understanding of science they have seen presented on television, when they do not. Mr Durnal cites one case of jurors in a murder trial who, having noticed that a bloody coat introduced as evidence had not been tested for DNA, brought this fact to the judge’s attention. Since the defendant had admitted being present at the murder scene, such tests would have thrown no light on the identity of the true culprit. The judge observed that, thanks to television, jurors knew what DNA tests could do, but not when it was appropriate to use them.

(...)

Criminals watch television too, and there is evidence they are also changing their behaviour. Most of the techniques used in crime shows are, after all, at least grounded in truth. Bleach, which destroys DNA, is now more likely to be used by murderers to cover their tracks. The wearing of gloves is more common, as is the taping shut—rather than the DNA-laden licking—of envelopes. Investigators comb crime scenes ever more finely for new kinds of evidence, which is creating problems with the tracking and storage of evidence, so that even as the criminals leave fewer traces of themselves behind, a backlog of cold-case evidence is building up.

The CSI effect can also be positive, however. In one case in Virginia jurors asked the judge if a cigarette butt had been tested for possible DNA matches to the defendant in a murder trial. It had, but the defence lawyers had failed to introduce the DNA test results as evidence. When they did, those results exonerated the defendant, who was acquitted.

Mr Durnal does not blame the makers of the television shows for the phenomenon, because they have never claimed their shows are completely accurate. (Forensic scientists do not usually wield guns or arrest people, for one thing, and tests that take minutes on television may take weeks to process in real life.) He argues that the CSI effect is born of a longing to believe that desirable, clever and morally unimpeachable individuals are fighting to clear the names of the innocent and put the bad guys behind bars. In that respect, unfortunately, life does not always imitate art.

The text above tells us that:

Item 2 - the defendant in the first murder trial mentioned denied his being present at the murder scene;

Julgue a alternativa:

Item 2 - Seja !$ h: \, \mathbb{R} \, \rightarrow \, \mathbf{R} !$ uma função contínua, tal que !$ (2 \chi \, - \, \pi)h(\chi) \, = \, 1 \, - \, sen \, \chi !$, para todo !$ \chi \, \in \, \mathbf{R}. !$ Então !$ h ( { \large \pi \over 2}) \, = \, 1. !$

Item 1 - the licking of envelopes is completely DNA-free;

We can infer from the text that:

Item 3 - nothing indicates that criminals are altering their behaviour;

[Para a resolução desta questão talvez lhe seja útil saber que se Z tem distribuição normal padrão, então Pr(|Z|>1,645)=0,10 e Pr(|Z|>1,96)=0,05.]

Considere as seguintes estimativas obtidas pelo método de mínimos quadrados ordinários para o modelo de regressão abaixo (desvios padrões entre parênteses):

ln(salário) = 0,600+ 0,175sindicato + 0,090sexo+0,080educ+0,030 exper – 0,003 exper²+!$ \hat{u} !$

(0,201) (0,100) (0,050) (0,032) (0,009) (0,001)

R² = 0,36

em que educ e exper denotam, respectivamente, o número de anos de estudo e o número de anos de experiência profissional, sindicato é uma variável dummy que assume o valor 1 se o trabalhador for sindicalizado e 0 caso contrário e sexo é uma variável dummy igual a 1 se o trabalhador for do sexo masculino e igual a 0 se for do sexo feminino. O resíduo da regressão é o termo !$ \hat{u} !$. Todas as suposições usuais acerca do modelo de regressão linear clássico são satisfeitas.

É correto afirmar que:

Item 1 - Supondo que o tamanho da amostra seja grande o suficiente para que aproximações assintóticas sejam válidas, é possível rejeitar, ao nível de significância de 5%, a hipótese nula de que os salários de homens e mulheres são iguais. A hipótese alternativa é que os salários de homens e mulheres são diferentes.