Numerade

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Exercise 14. Let $X_1, X_2, \dots, X_n$ be independent normal random variables with means $\mu_i$ and variances $\sigma_i^2$. Show that $Y = \sum_{i=1}^n \alpha_i X_i$, where the $\alpha_i$ are scalars, is normally distributed, and find its mean and variance. (Hint: Use moment generating functions.)

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When confronted by the young Phaeacian nobles, how does Odysseus answer their challenge?

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True or false: If F and G are both antiderivatives of the same function f on the interval (a, b), then F(x) = G(x) for all x in that interval.

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3. Find an approximate value of $ \log _{e} 5 $ by calculating to 4 decimal places, by Simpson's $ 1 / 3 $ rule, $ \int_{0}^{5} \frac{d x}{4 x+5} $, dividing the range into 10 equal parts: $ \left(\right. $ Anna $ _{\text {, }} $ 2005)

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Suppose country ABC and country XYZ both produce only apples and oranges. They each have the following production possibilities functions: ABC: Apples = 10 - (2/3) Oranges XYZ: Apples = 10 - Oranges a. If there was free trade between these 2 countries, what might happen? b. If there was free trade between these 2 countries, determine the price range of apples and oranges. c. In a free trade situation between these countries, the exchange rate is 1 orange for 0.75 apples. Suppose ABC wants to consume 6 apples and XYZ wants to consume 4 apples. Determine the gains from trade for each country.

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For this circuit: a.) Determine the time constant, $\tau$, and the steady state capacitor voltage, $v(\infty)$, when the switch is open. $\tau$ = ____ ms and $v(\infty)$ = ____ V b.) Determine the time constant, $\tau$, and the steady state capacitor voltage, $v(\infty)$, when the switch is closed. $\tau$ = ____ ms and $v(\infty)$ = ____ V

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Problem 6: The van der Pol oscillator, given by cu = v + u^3, exhibits periodic relaxation oscillations. The oscillation exhibits two time scales (a fast and slow time scale) for small e. Let f(u) = u^3/3 - u. The following information about f may be helpful: f'(1) = 0 f(1) = +2/3 f(2) = 2/3 (a) Draw the nullclines in the phase plane (uv-plane), sketch the limit cycle for small e, and label the regions of fast and slow dynamics on the limit cycle. (b) Compute the period of the oscillation at leading order as e approaches 0.

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There is one question for this forum with several parts that you should comment on: Think of someone you know who has suffered some kind of damage to the nervous system. If you do not know anyone like that, think of a movie that you have seen that has portrayed a person with this kind of injury or a famous person you have heard of who has a condition that affects the nervous system. Discuss the following: What was the nature of the problem (what kind of impact did it have on the person's abilities)? What was the cause (e.g., accident, tumor, disease like Alzheimer's)? What sorts of tests did the person undergo to determine the biological underpinnings of the problem? What part(s) of the nervous system were affected? Any other comments related to the relationship between the nervous system and behavioral/psychological functioning.

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03-Dadas as matrizes abaixo determine: $\begin{pmatrix} 1 & -1 & 0 \ 2 & 3 & 4 \ 0 & 1 & -2 \end{pmatrix}$ a) det 2.A = $B = \begin{pmatrix} -2 & 5 \ 6 & -7 \end{pmatrix}$ b) det B² =

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Consider the right triangle plotted on the grid below. If the slope of side $AB = \frac{4}{9}$, what would be the slope of side AC?

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robert g.