Numerade

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The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a highly left skewed distribution. Suppose we assume that session times on a web site for a visitor has a Pareto distribution with minimum session time = θ seconds while the connection is established and the first page delivered. The maximum length of the session is dependent on the degree of interest the visitor has in the material. Suppose Y1, Y2, . . . , Yn is a random sample of session times of n visitors, where each Yi has a Pareto density: fθ(y) = 3θ^3y^(−4), y ≥ θ; and 0, y < θ. for an unknown θ > 0. We are interested in the estimation of θ. (e) Derive the value of an that makes an bθ an unbiased estimator of θ. (f) Find the distribution function of bθ θ , and use it to explain why bθ θ is a pivotal quantity. (g) Using this pivotal quantity, derive a statistic bθL such that P (bθL ≤ θ) = 0.9. That is, determine a 90% LCB for θ. (h) Find the method of moments estimator (MOM) of θ. Is this estimator unbiased?

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Exercise C. Look for "chiral" carbons in the following. Label each chiral atom with the symbol *. These are the constitutional isomeric "pentanols", each is $ \mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O} $. (5 pts)

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Question 5 Find a counterexample to show that the statement is false. Every month of the year has 30 or 31 days. February Question 6 Find a counterexample to show that the statement is false. For every positive integer x, $x^3 < 2^x$. Question 7

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Session 9 children who think they are unlikeable at age _____ need adult about help with their social emotional development ?

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Which is true regarding surface tension? it results from the attraction of water molecules to air its effect is increased by surfactant it promotes the collapse of small alveoli its effect on lung compliance is small

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Part I Answer all questions in this part. 1. Compute the general solution of each of the following: (a) (6 points) $\frac{dy}{dx} = x + xy^2$ Show your work in this box: Write your answer in this box: (b) (6 points) $y'' + 4y' + 4y = 4 - 12e^{-2x}$ Show your work in this box:

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#3) The two middle rows of a Routh table is given as: .... 1 2 1 3 2 4 0 1 Can you finish the table, why?

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PART II: GAME THEORY A few months ago, Samsung revealed their new smartphone whose screen folds and unfolds according to the users' preferences. This addition seems so promising and profitable that Apple is planning to enter the market for foldable smartphones as well and is deciding on its production scale. Naturally, Samsung is ready to respond and should decide which pricing structure is the most convenient: setting a high price (accommodate) or starting a price war. The payoffs (in millions of dollars) for both companies are shown in the following payoff matrix: Samsung Accommodate Price War 67 32 Enter on Small Scale 13 7 Apple 18 25 Enter on Large Scale 15 s Here, Apple's payoffs are in the lower left of each box, Samsung's payoffs are in the upper right. (a) If both firms move simultaneously, does either firm have a dominant strategy? Explain. (b) Is there a pure strategy Nash equilibrium given that both firms move simultaneously? What is Apple's profit? (c) If Apple has a head start over Samsung (meaning they get to make their decision first), what is the new Nash equilibrium? What is Apple's profit? Draw a decision tree to show your argument. (d) Suppose now that a consultant tells Apple's CEO that the company can strictly improve its situation relative to part (b) by not entering this new market and instead choosing to run advertisements critical of Samsung's new product (bash the product). This adds a third possible strategy for Apple, but unfortunately, Apple's current CEO doesn't know all the potential payoffs - he's no Steve Jobs. The new matrix is depicted below. What values can these unknown parameters z and y take such that the consultant's claim is correct? Here, Apple and Samsung move simultaneously. Samsung Accommodating Price War 67 32 Enter on Small Scale 13 7 18 25 Enter on Large Scale 15 9 45 y Bash New Product 10 a

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$\text{V}_{in}$ \newline 10 V rms \newline $L = 1.0 \text{ mH}$ \newline $R_w = 10 \Omega$ \newline $C$ \newline $0.0022 \mu F$ \newline $R$ \newline $100 \Omega$ \newline $\text{V}_{out}$

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Which of the following statements is true? I bought a stock on margin at the price of $100, my maximum loss is unlimited. If I purchase and bond and hold it until maturity, my annualized holding period return is the same as the yield to maturity. A risk averse investor will not short sell a stock because short-selling is a very risky strategy. None of the statements provided is true.

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michael h.