Considere dois agentes, !$ i \, = \, 1,2, !$ que estão decidindo a que velocidade chegam a um destino.

Cada um deles possui uma função utilidade !$ U_i(v_i) \, = \, 2 \, \times \, v_i !$ em que !$ v_i !$ é a velocidade que eles estão trafegando. Só que, quanto mais rápido eles andam pela estrada, maior a probabilidade de ocorrência de um acidente, que é denotada por !$ p(v_1, \, v_2), !$ e que dá a eles um custo de !$ 0,5 !$ cada. A partir destas afirmações, responda V ou F a alternativa a seguir.

Item 1 - Se o agente for multado na eventualidade de um acidente, a velocidade em que ele trafega é maior.

Julgue a alternativa:

Item 3 - Se P(B) = 0,6 e P(A|B) = 0,2, então P(A^c !$ \cup !$B^c) = 0,88.

Text 2

Excerpts from:

Small eruption in Iceland

A cloud of ash from an Icelandic volcano shut European airspace for several days. Our first article examines the science of volcanic emissions.

Our second looks at the past week's disruption of travel

Apr 22nd 2010 | From The Economist print edition

SOME natural disasters, like the Indian Ocean tsunami of 2004, strike out of the blue. Only with hindsight do they come to look like the sort of thing people should have been prepared for. Other events get dress rehearsals. The eruption of Eyjafjallajokull in the south of Iceland was one of these. In February 2008 officials from air-traffic-control services across Europe, as well as representatives of weather services and airlines, ran an exercise that simulated a strikingly similar eruption. The volcano they chose was not Eyjafjallajokull, but its neighbour, Katla; the weather conditions were not quite the same. But the procedures were.

(...)

If the exercise two years ago did not capture the range of problems that an Icelandic volcano might cause, it did show that the general situation was entirely foreseeable. A ridge of submerged mountains runs down the middle of the Atlantic Ocean; Iceland is the result of a “hotspot” in which material rises from deep within the Earth, pushing part of this ridge up into the air. Both hotspots and mid-ocean ridges are volcanic, so Iceland is doubly so. It boasts a fearsome array of volcanoes, 33 of which have erupted once or more since the end of the last ice age, around 12,000 years ago.

As these volcanoes go, Eyjafjallajokull is neither very big nor particularly prolific. It has erupted only three times since Iceland was settled in the ninth century. That is why the air-traffic exercise planners chose Katla, 25km (16 miles) away; it typically erupts every 30-80 years, and in a much more spectacular way. But a combination of circumstances meant that, though comparatively small, Eyjafjallajokull's current eruption punched above its weight in the ash-production league in its early days, emitting much more fine ash than is normal. Fine ash can travel farther than the heavier stuff, but still does a lot of harm to engines if encountered in significant quantities.

(...)

Katla is not the worst that Iceland can do. Its volcanoes do not have the explosive oomph of some eruptions in the “ring of fire” around the Pacific, such as those of Tambora and Krakatoa in the 19th century, let alone the prehistoric eruptions of Taupo, in New Zealand, and Toba, in Indonesia, which were large enough to have severe, if short-lived, effects on the global climate (...) But the eruption of Oraefajokull, in the south-east of the island, in 1362 is thought by some to have eclipsed that of Mount Vesuvius which destroyed Pompeii and Herculaneum in 79AD. It may have been the biggest bang in Europe since the eruption in the 17th century BC of Santorini, which devastated the Minoan civilisation on nearby Crete. Nor is explosive power the only measure of a volcano's spitefulness. The eruption of Laki, an Icelandic volcanic fissure, in 1783 sent poisonous gases across Europe.

Another concern is that Iceland's volcanoes, especially those under its central ice cap—which, other things being equal, will produce more explosive plumes if they break through—seem to show a cycle in activity, perhaps due to the hotspot that feeds them.

On this reading of the record, activity can be expected to increase for the next 40 years or so. The past few decades have been one of the quiet patches. It seems likely that the first 50 years of jet travel across the North Atlantic enjoyed particularly clear skies.

According to the text, Eyjaffallafokull's current eruption:

Item 3 - is only one of three since the end of the ice-age 12,000 years ago;

Julgue a seguinte alternativa:

Item 1 - De acordo com a Lei de Okun, um aumento de 1% no PIB está associado a uma redução de 1% na taxa de desemprego.

No que concerne ao Plano de Metas do Governo Kubitschek (1956-1960) e à industrialização brasileira no período, pode-se afirmar o seguinte:

Item 2 - A liderança do crescimento no período coube às atividades produtoras de insumos intermediários.

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

Item 3 - Se !$ \mid v f (a, \, b) \mid \, \ne \, 0 !$ e a derivada direcional de !$ f !$ no ponto !$ (a, \, b) !$ na direção do vetor unitário u é zero, então !$ v f (a, \, b) !$ e u são paralelos.

Considere as transformações lineares !$ T \, : \, \mathbf{R}^3 \, \rightarrow \mathbf{R}^3 !$ e !$ L \, : \, \mathbf{R}^3 \, \rightarrow \, \mathbf{R}^3 !$ definidas por

!$ T \, \begin {pmatrix} \chi \\ y \\ z \end {pmatrix} \, = \, \begin {pmatrix} 2\chi \, - \, 2y \, + \, 3z \\ 3y \, - \, 2z \\ -y \, + \, 2z \end {pmatrix} e L \, \begin {pmatrix} \chi \\ y \\ z \end {pmatrix} \, = \, \begin {bmatrix} 1 \,\, 0 \,\, 1 \\ 1 \,\, 1 \,\, 2 \\ 2 \,\, 1 \,\, 3 \end {bmatrix} \, \begin {pmatrix} \chi \\ y \\ z \end {pmatrix}. !$

Seja A a matriz de T relativa à base canônica de !$ \mathbf{R}^3 !$. Julgue a alternativa:

Item 0 - L é sobrejetora.

[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 4 - Supondo que os erros tenham distribuição normal e que o tamanho da amostra seja 206, é possível rejeitar, ao nível de significância de 5%, a hipótese de que os coeficientes da regressão, com exceção do intercepto, são simultaneamente iguais a zero (F_{0,95; 5, 200} = 2.2592).