Sejam X e Y duas variáveis aleatórias e

I. E(X) e E(Y) as expectâncias de X e Y, respectivamente;

II. Var(X) e Var(Y) as variâncias de X e Y, respectivamente;

III. Cov(X,Y) a covariância de X e Y.

Tem-se, em qualquer situação,

A média aritmética dos valores das vendas diárias realizadas pelas 50 empresas do Setor A é de R$ 1 000,00, com desvio padrão de R$ 100,00. Sabe-se ainda que a média aritmética dos valores das vendas diárias realizadas pelas 200 empresas do Setor B é de R$ 2.000,00, com desvio padrão de R$ 200,00. A variância em (R$)² dos valores das vendas diárias realizadas pelos dois setores reunidos é

Um empresário, investindo em um determinado empreendimento, espera ter os seguintes lucros em função dos cenários "Bom", "Médio" e "Ruim":

A expectância e a variância do respectivo lucro são, em R$ e (R$)² , respectivamente,

Do total de títulos em poder de um investidor, !$ 1 \div 8 !$ é do tipo T₁, !$ 1 \div 4 !$ é do tipo T₂ e o restante do tipo T₃. Sabe-se que as probabilidades de se obter uma taxa real de juros positiva com estas aplicações são 0,60 com T₁, 0,70 com T₂ e 0,80 com T₃. Se for escolhido um título aleatoriamente entre estes em poder do investidor e verificarem-se que apresentou uma taxa real de juros não positiva, a probabilidade dele ser do tipo T₃ é

Uma variável aleatória contínua X tem a seguinte função densidade de probabilidade:

!$ f(x)= \begin{cases} 0, & \mbox {se } x < 0 \\ {x \div 12} + K, & \mbox {se } 0 \le x \le 3\\ 0, & \mbox {se } x > 3 \end{cases} !$

Sendo K uma constante, seu valor é igual a

Senate Passes Plan to Cut $35 Billion From Deficit

The Senate approved sweeping deficit-reduction legislation last night that would save about $35 billion over the next five years by cutting federal spending on prescription drugs, agriculture supports and student loans, while clamping down on fraud in the Medicaid program.

The measure would also open Alaska's Arctic National Wildlife Refuge to oil drilling, a long-sought goal of the oil industry that took a major step forward after years of political struggle. A bipartisan effort to strip the drilling provision narrowly failed.

The Senate bill, which passed 52 to 47, is the first in nearly a decade to tackle the growth of entitlement spending, the part of the federal budget that rises automatically based on set formulas and population changes. It would shave payments to some farmers by 2.5 percent, while eliminating a major cotton support program and trimming agriculture conservation spending. A proposal to limit payments to rich farmers failed yesterday. The measure passed largely along party lines, with only two Democrats voting for it and five Republicans voting against it.

Yesterday's action is part of an effort by congressional Republicans to demonstrate fiscal discipline after widespread complaints of profligate spending on Capitol Hill. ... ⁵¹ many Democrats and some moderate Republicans are concerned that the effort may go too far, prominent Republicans in the Senate and House said the cuts were necessary to slow the rate of spending and control a deficit projected to total $314 billion by the end of the fiscal year.

During a speech yesterday, former House majority leader Tom Delay (R-Tex) repeatedly apologized for excessive spending by Congress, including recent highway legislation that was ...⁵² with lawmakers' pet projects. After noting that House Republicans have voted to cut taxes every year since winning the majority in 1994, DeLay acknowledged, "Our record on spending has not been as consistent, ...⁵³ ."

(Adapted from washingtonpost.com)

Senate Passes Plan to Cut $35 Billion From Deficit

The Senate approved sweeping deficit-reduction legislation last night that would save about $35 billion over the next five years by cutting federal spending on prescription drugs, agriculture supports and student loans, while clamping down on fraud in the Medicaid program.

The measure would also open Alaska's Arctic National Wildlife Refuge to oil drilling, a long-sought goal of the oil industry that took a major step forward after years of political struggle. A bipartisan effort to strip the drilling provision narrowly failed.

The Senate bill, which passed 52 to 47, is the first in nearly a decade to tackle the growth of entitlement spending, the part of the federal budget that rises automatically based on set formulas and population changes. It would shave payments to some farmers by 2.5 percent, while eliminating a major cotton support program and trimming agriculture conservation spending. A proposal to limit payments to rich farmers failed yesterday. The measure passed largely along party lines, with only two Democrats voting for it and five Republicans voting against it.

Yesterday's action is part of an effort by congressional Republicans to demonstrate fiscal discipline after widespread complaints of profligate spending on Capitol Hill. ... ⁵¹ many Democrats and some moderate Republicans are concerned that the effort may go too far, prominent Republicans in the Senate and House said the cuts were necessary to slow the rate of spending and control a deficit projected to total $314 billion by the end of the fiscal year.

During a speech yesterday, former House majority leader Tom Delay (R-Tex) repeatedly apologized for excessive spending by Congress, including recent highway legislation that was ...⁵² with lawmakers' pet projects. After noting that House Republicans have voted to cut taxes every year since winning the majority in 1994, DeLay acknowledged, "Our record on spending has not been as consistent, ...⁵³ ."

(Adapted from washingtonpost.com)

Dentre as alternativas abaixo, qual delas NÃO representa o sentido com que entitlement em entitlement spending é usado no texto?

Senate Passes Plan to Cut $35 Billion From Deficit

The Senate approved sweeping deficit-reduction legislation last night that would save about $35 billion over the next five years by cutting federal spending on prescription drugs, agriculture supports and student loans, while clamping down on fraud in the Medicaid program.

The measure would also open Alaska's Arctic National Wildlife Refuge to oil drilling, a long-sought goal of the oil industry that took a major step forward after years of political struggle. A bipartisan effort to strip the drilling provision narrowly failed.

The Senate bill, which passed 52 to 47, is the first in nearly a decade to tackle the growth of entitlement spending, the part of the federal budget that rises automatically based on set formulas and population changes. It would shave payments to some farmers by 2.5 percent, while eliminating a major cotton support program and trimming agriculture conservation spending. A proposal to limit payments to rich farmers failed yesterday. The measure passed largely along party lines, with only two Democrats voting for it and five Republicans voting against it.

Yesterday's action is part of an effort by congressional Republicans to demonstrate fiscal discipline after widespread complaints of profligate spending on Capitol Hill. ... ⁵¹ many Democrats and some moderate Republicans are concerned that the effort may go too far, prominent Republicans in the Senate and House said the cuts were necessary to slow the rate of spending and control a deficit projected to total $314 billion by the end of the fiscal year.

During a speech yesterday, former House majority leader Tom Delay (R-Tex) repeatedly apologized for excessive spending by Congress, including recent highway legislation that was ...⁵² with lawmakers' pet projects. After noting that House Republicans have voted to cut taxes every year since winning the majority in 1994, DeLay acknowledged, "Our record on spending has not been as consistent, ...⁵³ ."

(Adapted from washingtonpost.com)

A partir de are concerned that the effort may go too far, depreende-se que esses políticos estão

Senate Passes Plan to Cut $35 Billion From Deficit

The Senate approved sweeping deficit-reduction legislation last night that would save about $35 billion over the next five years by cutting federal spending on prescription drugs, agriculture supports and student loans, while clamping down on fraud in the Medicaid program.

The measure would also open Alaska's Arctic National Wildlife Refuge to oil drilling, a long-sought goal of the oil industry that took a major step forward after years of political struggle. A bipartisan effort to strip the drilling provision narrowly failed.

The Senate bill, which passed 52 to 47, is the first in nearly a decade to tackle the growth of entitlement spending, the part of the federal budget that rises automatically based on set formulas and population changes. It would shave payments to some farmers by 2.5 percent, while eliminating a major cotton support program and trimming agriculture conservation spending. A proposal to limit payments to rich farmers failed yesterday. The measure passed largely along party lines, with only two Democrats voting for it and five Republicans voting against it.

Yesterday's action is part of an effort by congressional Republicans to demonstrate fiscal discipline after widespread complaints of profligate spending on Capitol Hill. ... ⁵¹ many Democrats and some moderate Republicans are concerned that the effort may go too far, prominent Republicans in the Senate and House said the cuts were necessary to slow the rate of spending and control a deficit projected to total $314 billion by the end of the fiscal year.

During a speech yesterday, former House majority leader Tom Delay (R-Tex) repeatedly apologized for excessive spending by Congress, including recent highway legislation that was ...⁵² with lawmakers' pet projects. After noting that House Republicans have voted to cut taxes every year since winning the majority in 1994, DeLay acknowledged, "Our record on spending has not been as consistent, ...⁵³ ."

(Adapted from washingtonpost.com)

No 3^o parágrafo, nearly pode ser substituído, sem alteração de sentido, por

Senate Passes Plan to Cut $35 Billion From Deficit

The Senate approved sweeping deficit-reduction legislation last night that would save about $35 billion over the next five years by cutting federal spending on prescription drugs, agriculture supports and student loans, while clamping down on fraud in the Medicaid program.

The measure would also open Alaska's Arctic National Wildlife Refuge to oil drilling, a long-sought goal of the oil industry that took a major step forward after years of political struggle. A bipartisan effort to strip the drilling provision narrowly failed.

The Senate bill, which passed 52 to 47, is the first in nearly a decade to tackle the growth of entitlement spending, the part of the federal budget that rises automatically based on set formulas and population changes. It would shave payments to some farmers by 2.5 percent, while eliminating a major cotton support program and trimming agriculture conservation spending. A proposal to limit payments to rich farmers failed yesterday. The measure passed largely along party lines, with only two Democrats voting for it and five Republicans voting against it.

Yesterday's action is part of an effort by congressional Republicans to demonstrate fiscal discipline after widespread complaints of profligate spending on Capitol Hill. ... ⁵¹ many Democrats and some moderate Republicans are concerned that the effort may go too far, prominent Republicans in the Senate and House said the cuts were necessary to slow the rate of spending and control a deficit projected to total $314 billion by the end of the fiscal year.

During a speech yesterday, former House majority leader Tom Delay (R-Tex) repeatedly apologized for excessive spending by Congress, including recent highway legislation that was ...⁵² with lawmakers' pet projects. After noting that House Republicans have voted to cut taxes every year since winning the majority in 1994, DeLay acknowledged, "Our record on spending has not been as consistent, ...⁵³ ."

(Adapted from washingtonpost.com)