Com respeito a inferência e estimação de parâmetros populacionais, é correto afirmar:

Item 4 - Suponha que x tenha distribuição N(!$ \mu;\sigma^2 !$) em que !$ \sigma^2 !$seja desconhecido. O intervalo de confiança para a média da população, !$ \mu !$, será !$ P\{\overline{x}-z\dfrac{\sigma}{\sqrt{n}} \ge \mu \ge \overline{x} + z \dfrac{\sigma}{\sqrt{n}}=2\Phi(z)-1 !$ é a função de distribuição Normal Padrão.

Sejam !$ A=\begin{pmatrix} 2&-1&-3\\1&-1&1\\-3&2&2\end{pmatrix}, \vec{x}=\begin{pmatrix}x_1\\x_2\\x_3 \end{pmatrix} !$e !$ \vec{b}=\begin{pmatrix}b_1\\b_2\\b_3 \end{pmatrix} !$. Assinale V (verdadeiro) ou F (falso):

Item 2 - se !$ A\vec{x}=\vec{b} !$, então !$ \vec{x}=A^{-1}\cdot \vec{b} !$;

A year later, the American economist, Hollis Chenery, was invited to Santiago to give the ECLA Lectures. His main concern was to stimulate interest in input-output analysis and linear programming for investment planning in developing countries. But he also made a spirited plea for structuralism:

“A central problem of development policy is the adequacy of free market forces in allocating investment resources.... The traditional view of economic policy in Western countries is derived from the classical theory of competitive equilibrium.... The main policy implication of this model is that, under static conditions of perfect competition, market forces will tend to bring about the best of a country’s resources.”

He pointed out that the Keynesian revolution, while successfully challenging classical theory in relation to short-term fluctuations in income and employment, had left its conclusions on longer-term resource allocation virtually unaffected. He identified departures from competition, dynamic causes and equity considerations as the ‘three kinds of defect in the free price-mechanism as an instrument for achieving the maximum social welfare and listed, under the first heading, such obstacles as inadequate information, restrictions on entry into occupations and limited access to capital.

“Theses factors combine to produce a rigid market structure, prevalent monopoly positions, immobile labor and capital, and consequently great inequalities in the returns to labor and capital in different uses... Serious structural disequilibrium in the use of labor, natural resources or foreign exchange represents one of the situations justifying state intervention in investment decisions.”

According to the text, Hollis Chenery

Item 4 - made an earnest request for Chileans to use input-output analysis.

Indique a afirmativa correta:

Item 0 - Um monopolista que seja capaz de praticar discriminação de preços de 1º grau pode exaurir a totalidade dos ganhos de troca do consumidor.

The classical and neoclassical thesis according to which, in a perfectly competitive economy and in the absence of externalities, market forces operating through the price mechanism assure an optimum allocation of resources, statically and dynamically, were open to attack at three points. First, prices may give the wrong signals because they are distorted by monopoly or other influences. Secondly, labor and other factors of production may respond to price signals inadequately or even perversely. Thirdly, although ready to respond appropriately to price signals, factors of production may be immobile, unable to move quickly if at all. Lets us call them the ‘signaling’, ‘response’ and ‘mobility’ components of the mechanism.

According to the text,

Item 3 - the factor immobility hypothesis trumpet up by critics of the market system is highly exaggerated.

Com respeito a inferência e estimação de parâmetros populacionais, é correto afirmar:

Item 2 - Suponha que a variável aleatória x seja uniformemente distribuída no intervalo [0, !$ \beta !$], em que !$ \beta !$ é um parâmetro desconhecido. O estimador de máxima verossimilhança de será !$ \hat{\beta}=mínimo[x_1,x_2, ......, x_n] !$.