Numerade

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An experiment produces random vector $\mathbf{X} = (X_1, \dots, X_k)^T$ with expected value $\boldsymbol{\mu_X} = (\mu_1, \dots, \mu_k)^T$. The $i$'th component of $X$ has variance $\text{Var}(X_i) = \sigma_i^2$. To estimate $\boldsymbol{\mu_X}$, we perform $n$ independent trials such that $\mathbf{X}(i)$ is the sample of $\mathbf{X}$ on trial $i$, and we form the vector mean $$ \mathbf{M}(n) = \frac{1}{n} \sum_{i=1}^n \mathbf{X}(i). $$ (a) Show $\mathbf{M}(n)$ is unbiased by showing $E(\mathbf{M}(n)) = \boldsymbol{\mu_X}$. (b) Show that the sequence of estimates $\mathbf{M}(n)$ is consistent by showing that for any constant $c > 0$, $$ \lim_{n \to \infty} P\left( \max_{j=1, \dots, k} |M_j(n) - \mu_j| \geq c \right) = 0. $$ Hint: Let $A_i = \{ |M_j(n) - \mu_j| \geq c \}$ and apply the union bound to upper bound $P(A_1 \cup A_2 \cup \dots \cup A_k)$. Then apply the Chebyshev inequality.

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Which of the following is NOT part of the financial accounting information system? a. filing reports with the SEC b. making a managerial assessment such as determining the future cash flows of a proposed flexible manufacturing system c. reporting a large contingent liability to current and potential shareholders d. preparing GAAP financial statements

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5. What would be the major product of the following reaction \[ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OCH}_{3} \xrightarrow[\text { heat }]{\text { Concd. } \mathrm{HBr}_{(x a)}} \text { ? } \] A) $ \mathrm{C}_{8} \mathrm{H}_{5} \mathrm{Br}+\mathrm{CH}_{3} \mathrm{OH} $ B) $ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{CH}_{3} \mathrm{Br} $ C) $ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{CH}_{3} \mathrm{Br} $ D) $ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{CH}_{3} \mathrm{OH} $ E) $ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br} $ 6. What would be the final product? $ (\mathrm{CH} 3) 2 \mathrm{CHCH} 2 \mathrm{OCH} 3 $ B) C) D) 7. What is the correct IUPAC name for the following compound? a) 4-isopropyl-3,4-dimethyl-2-butanol b) 2,3,4-trimethyl-4-pentanol c) 1,1,2,3-tetramethyl-4-pentanol d) 3,4,5-trimethyl-2-hexanol e) 3,4,5,5-tetramethyl-2-pentanol

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A nurse us providing teaching for a client who has insomnia and a new prescription for ramelteon. Which of the following information should the nurse include?

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FIGURE 9-3 The following diagram contains information on cost and revenue curves facing a regulated monopoly. Price P1 P2 P3 P4 P5 P6 AC MC MR Q1 Q2 Q3 Q4 Quantity Refer to Figure 9-3. If the government is able to regulate the monopolist using marginal-cost pricing, what price and output combinations are expected to result? a. P2 and Q2 b. P5 and Q2 c. P3 and Q1 d. P6 and Q4

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Calculate $\int_0^t x^3 e^{-3x} dx$.

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Obtain (a) Fourier Sine Series (give me the step by step procedure) (b) Fourier Cosine Series over interval 0 < x < π; function f(x)=sin(3x) Sketch the function for (a) and (b) that is the sum of the series obtained. (give me the step by step procedure of every question)

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The map below shows the total dollar amount received for each tax dollar sent by county in Washington State in 2010. A researcher believes that: (i) Generally, counties receiving more revenue from the state than they had sent (as measured by the total dollar amount received for each tax dollar sent) tend to be those which voted for Republican. More importantly, he has argued that (ii) those receiving far higher revenue per tax dollar sent i.e. $1.5 or more (as shown in the map) are associated with "deep red" counties (which voted 61-70% for Republican). You have decided to find out if (ii) above is true (i.e. if such an association exists) by performing a statistical test. Show your method. Revenue/Tax Disparities by County in 2010 SAN JUAN $0.46 WHATCOM $0.97 SKAGIT $0.85 OKANOGAN FERRY PEND OREILLE $1.97 ISLAND $1.10 SNOHOMISH $0.99 SNEASIS $1.29 $1.05 DOUGLAS LINCOLN SPOKANE $1.35 KITSAP $1.28 $0.62 GRAYS HARBOR $1.63 KITTITAS GRANT PIERCE $1.25 $1.15 $1.59 PACIFIC $1.52 LEWIS COWLITZ $1.47 BENTON SKAMANIA $1.42 WALLA WALLA ASOTIN $2.30 $2.08 CLARK $1.39 KLICKITAT $1.98 How each county votes 51-60 Republican 61-70 Republican 51-60 Democrat ET 61-70 Democrat 50/50 Split

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For the right triangles below, find the exact values of the side lengths $d$ and $c$. If necessary, write your responses in simplified radical form.

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Assume that the production function takes the form, F(K, N) = K$^\alpha$N$^{1-\alpha}$, while $\delta$ = 1 and the momentary utility takes the following functional form: u(C) = log C. (a) (10 points) Solve for the competitive equilibrium level of capital accumulation, K$_2$. (b) (6 points) How does capital accumulation respond to an increase in the discount factor $\beta$? How does consumption respond in each period? Explain intuitively. (c) (8 points) How does capital accumulation respond to an increase in the tax rates, $\tau_t$ for t = 1, 2? How does consumption respond in each period? Explain intuitively.

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joseph k.