Suponha que !$ X_1 !$, !$ X_2 !$, ... , !$ X_n !$ sejam identicamente distribuídas, tendo valor esperado e variâncias comuns dados por !$ μ !$ e !$ σ^2 !$, respectivamente. Defina a variância amostral como !$ s^2 = (n-1)^{-1} \sum_{k=1}^n (Xk - \overline{X} )^2 !$, e considere a seguinte assertiva:

(I) A média amostral é um estimador consistente de !$ μ !$.

(II) A variável !$ (n-1)S^2/ σ^2 !$ tem distribuição de qui-quadrado com n-1 graus de liberdade.

(III) !$ S^2 !$ é estimador não-tendencioso de !$ σ^2 !$.

(IV) A média amostral tem distribuição normal.

Podemos afirmar que:

Item 1: A assertiva (III) é correta mesmo sem a hipótese de normalidade de !$ X_1 !$, !$ X_2 !$, ... , !$ X_n !$.

Indique se a afirmativa abaixo é verdadeira ou falsa:

Item 3: !$ \int\limits_{- \infty}^{+ \infty} !$ xdx = 0

Considere um espaço amostral com a terna , onde é o conjunto universo, é o conjunto dos possíveis eventos e P é uma medida de probabilidade. Podemos afirmar que:

Item 1: Se Y = aX + b, onde a, b > 0 são constantes, então Y é uma variável aleatória e sua função de densidade é !$ g(y) = { \large 1 \over a} f ( { \large y - b \over a}) !$.

Indique a afirmativa verdadeira e falsa:

Considere as matrizes A e B, ambas quadradas de ordem n. Afirma-se:

Item 6: Se A e B são não singulares, então !$ (AB)^{-1} = A^{-1} B^{-1} !$.

Indique se a afirmativa abaixo são verdadeira ou falsa:

Item 0: Uma função !$ f: \Re \rightarrow \Re !$ duas vezes derivável é estritamente côncava se, e somente se, a sua derivada segunda é estritamente negativa.

Dada a equação diferencial !$ y'' + 2y' + 2y = 1 !$, indique se a afirmativa abaixo é verdadeira ou falsa:

Item 1: !$ y(t) = 1/2 !$ é a única solução estacionária (i.e., constante) da equação.

Tight Money
By

Robert Heilbroner and Lester Thurow. Economics Explained. Chapter 12, pp. 158-159. Touchstone Book. Simon and Schuster, 1994.

That bring us, of course, back to square one. If we cannot easily introduce deep institutional changes and if the use of controls promises quick relief but no permanent cure, how do we cope with the inflationary propensities that continue to lurk within modern capitalism?

The answer is very likely to be continued reliance on the one medicine that has brought inflationary fever down: tight money. As we have seen, if we are willing to tighten money ruthlessly, and to keep it tight until unions quit asking for higher wages and corporations are forced into price wars to win markets, then inflation will come to an end.

The problem with tight money is twofold. The first, obvious, problem is that the cure is so severe it threatens the health of the patient, even though it rids him of his immediate ailment. The recession that stopped inflation in the early 1980s was the worst economic catastrophe that afflicted the capitalist world since the Great Depression itself. No one wants to go through that experience again.

The second problem with tight money is certainly not an equitable, and likely not an effective anti-inflationary policy unless it is imposed with Draconian severity. Suppose a tight-money policy brings unemployment up to, say, 8 percent. That does not mean that every worker is laid off for 8 percent of the year. It means that some workers are unemployed for long periods of time. Over 50 percent of the total number of weeks of unemployment is typically borne by individuals who are unemployed for more than half of the year. Almost half of those who suffer long spells of unemployment end up not with a job, but by withdrawing from the work force.

Thus if a relatively mild recession is the way we decide to fight inflation, we should recognize that the honor of being designated as an inflation fighter is rather selectively awarded. It does not mainly go to those whose recruitment into the brigade of the unemployed would be most effective in bringing down wage rates, namely the group of prime-age white males. Rather, enlistment in the ranks of inflation fighters is predominantly that of younger workers, age 16-24, of women, of blacks and of Hispanics. These groups share two characteristics: they tend to be relatively unskilled, and they tend to lack political clout. Thus their impact on the trend of the national wage rate is small. The brigade is not only inequitably chosen, but is ineffective.

The authors argues that given the inability to make deep institutional changes, tight money stops inflation,

Item 4: but the government should take measures to protect labor unions.