Numerade

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Problem 2: Exponential Maximum Likelihood Estimation (20pts) Consider a nonnegative, real-valued random variable $X$ that is distributed according to an exponential distribution $X \sim \lambda e^{-\lambda x}$ for some real-valued parameter $\lambda > 0$ and $x \ge 0$. 1. Given data samples $x^{(1)}, \dots, x^{(m)}$, what is the maximum likelihood estimate for $\lambda$? 2. Give an example of a prior such that the maximum likelihood estimate of $\lambda$ does not converge to the true value as the number of data observations goes to infinity. 3. Suppose we use the Gamma distribution as a prior probability distribution for $\lambda$: $\lambda \sim \frac{\beta^\alpha}{\Gamma(\alpha)} \lambda^{\alpha - 1} e^{-\beta \lambda}$, where $\alpha, \beta > 0$ are parameters of the prior and $\Gamma(\alpha)$ is the normalizing constant. What is the MAP estimate under this choice of prior? Does the MAP estimator converge to the MLE as the number of data observations tends towards infinity?

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The standard Gibbs free energy for the hydrolysis of ATP to ADP is -31 kJmol-1 . What is the Gibbs energy of reaction in an environment at 37 \deg C in which the ATP, ADP, and Pi concentrations are (a) 1.0 mmol dm-3 and (b) 1.0 mmol dm-3 ?

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R1 a b I1 R2 V+ C R3 R1 = 9 k? R2 = 9 k? R3 = 1 k? The measured nodal voltages are: Va = 18 V Vb = 9.521052631578948 V Vc = 1.0421052631578949 V Find voltage $V_{ab}$ and the current $I_1$. $V_{ab}$ = ____ V $I_1$ = ____ mA (within three significant digits) Is What is the power for the voltage and current source in watts? $P_{Vs}$ = ____ W $P_{Is}$ = ____ W (within three significant digits)

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What percentage of daughter atoms remain after 2 half-lives have elapsed? ? 25% ? 75% ? 100% • 50%

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Why does the Sun appear to rise and set in our sky? The Earth rotates. The Earth revolves. The Sun goes around the Earth once per day.

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If firm 'A' (worth $900,000 by itself) acquires firm 'B' at an acquisition cost of $400,000 (paying zero premium) and claims to be able to extract $100,000 in annual economies of scope, then which of the following market values is the best approximation of a value that reflects a market belief that firm 'A' actually can extract at least $100,000 in annual economies of scope? In other words, what will the new combined value of firms 'A' and 'B' be AFTER firm 'A' acquires firm 'B' and successfully convinces the market they have achieved the $100,000 of economies of scope? (Assume a WACC of 7.0% for all firms involved both before and after the acquisition). $1,300,000 $1,828,571 $2,328,571 $1,428,571 Correct! $2,728,571 $5,714,286 $1,400,000 $1,928,571 $1,307,000 $1,500,700

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Implement an insert member function that places the next node at the end of the list. (This is different than what I discussed in class). Implement a find member function that finds a specified data element in a linked list. Implement an insertAfter member function that inserts data after a given data value, such as insertAfter(2, 3) where 3 is inserted after 2. Implement a remove(data) member function that removes a specified data value from a linked list. C++

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Which establishes a system in which the state holds all power over the social order? theocracy authoritarian governments fascism totalitarianism

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Convert 7.44x10^4 µL to dm^3 using the conversion table below: Metric Prefixes Conversion Factors Volume Conversions Name Symbol Value 1 in 2.54 cm 1 ft 12 in 1 mi 5,280 ft 1 mi 1.609344 km 1 m 39.37 in 1 lb 453.6 g 1 kg 2.205 lbs 1 gal 3.785 L 1 L 1.0567 qt 1 mi/hr 0.4470 m/s 1 cal 4.184 J 1 L-atm 101.325 J 1 atm 14.70 psi 1 atm 101325 Pa 1 atm 760 torr (~mmHg) 1 bar 105 Pa 1 L = 1 dm^3 1 L = 1000 mL 1 mL = 1 cm^3 1 mL = 1000 L 1 m^3 = 1000 L 1 m^3 = 10^6 cm^3 tera- 10^12 giga- 10^9 mega- 10^6 kilo- 10^3 base unit 1 deci- 10^-1 centi- 10^-2 milli- 10^-3 micro- 10^-6 nano- 10^-9 pico- 10^-12 femto- 10^-15 atto- 10^-18 = exact

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Solve the equation over the given interval. cos(2x) - cos(x) = 4sin (x) - 4, imes [0, 2n]

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courtney r.