Numerade

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8) (15 marks) Let $ \left(x_{1}, x_{2}, \ldots, x_{n}\right) $ be i.i.d. samples from a Poisson distribution with unknown parameter $ \lambda $, where $ \lambda>0 $. Note that the probability mass function of a Poisson random variable is: \[ f_{X}(x)=\frac{\lambda^{x} e^{-\lambda}}{x!}, x=0,1,2, \ldots \] (a) (10 marks) Find the maximum likelihood estimate (MLE) of $ \lambda $. Page 2 of 3 (b) ( 5 marks) Let the prior distribution of $ \lambda $ be a Gamma distribution with the following density function: \[ \pi(\lambda)=\left\{\begin{array}{cc} \frac{\beta^{\alpha} \lambda^{\alpha-1}}{\Gamma(\alpha)} e^{-\beta \lambda}, \lambda>0 \\ 0 & , \lambda \leq 0 \end{array}, \text { where } \alpha>0 \text { and } \beta>0\right. \] Find the maximum a posteriori (MAP) estimate of $ \lambda $.

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3) for structures a-d, complete the corresponding Fischer projections, shown on the right-hand side. a) b) c) d) H H OH Cl CH$_3$ CH$_3$ CH$_3$ CH$_3$ H HO H Cl CH$_3$ CH$_3$ H- OH HO OH Br Br CH$_2$CH$_3$

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Question 6 The financial friction is the: result of adding the inflation rate to the unemployment rate. interest rate used in subprime loans. variance of the risk-free interest rate. difference between long-run inflation and the actual rate of inflation. difference between the federal funds rate and interest rates in financial markets. 3 pts

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Alberta Pasta is considering producing a new type of pasta. The required equipment has a constant capital cost allowance over its 3-year life with a zero salvage value. No new working capital would be required. Revenues and cash operating costs are expected to be constant over the project's 3-year life. However, this project would compete with other Alberta Pasta products and would reduce the company's pre-tax annual cash flows. What is the project's NPV? WACC 10.0% Pre-tax cash flow reduction in other products 15,000 Net investment in fixed assets 65,000 Annual capital cost allowance 31,000 Sales revenues, each year 80,000 Cash operating costs, each year 25,000 Tax rate 25.0% O a. 93,879 O b. 37,750 O c. 28,879 O d. 29,325

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For the cantilever beam shown, determine the reactions at the fixed end. The length of the beam is $L = 3$ ft. (Enter forces in kips and moment in ft \cdot kips.) $w(x) = (65 \text{ kips/ft}) \cos(\frac{\pi x}{2L})$ $A_x$ magnitude ---Select--- kips direction $A_y$ magnitude ---Select--- kips direction $M_A$ magnitude ---Select--- ft \cdot kips direction

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Q1: For each of the molecules determine the number of modes, the number of stretching modes, and the number of bending modes. For each molecule describe one oscillation-mode and justify why it is (is not) IR-active. a) H? b) HCl c) HCN (see below) d) AlF3 (analyse two modes: 1- a breathing mode, 2- where two F's 'swing' in a 'scissor-mode'). H C N 180° H C N

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QUESTION 6 50 points Save Answer A 0.2 m thick plane wall ($k = 10 \frac{W}{mC}$) has internal heat generation at a rate of $1.5 \times 10^5 \frac{W}{m^3}$. The temperature on both sides of the wall is 50C. Calculate the temperature 0.05m into the plane wall. Include a schematic labeled with L for full credit.

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10. If x stands for the measure of the smaller angle, which of the following equations will help you solve the problem? a. $x + (x + 20) = 90$ b. $x + 20x = 90$ 11. What is the measure of the smaller angle? c. $x + (x + 20) = 180$ d. $x + 20x = 180$

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System of inequalities: Y â‰¤ 3x + 6 y â‰¤ 3x + 6 4y + 3x < 3 x - 2xz - 2 a. Name the coordinates of the vertices of the feasible region: vertices: b. Find the maximum and minimum values of the following function for this region: f(xy) = -x + 3y

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at the right. Use the graph at the right to answer 1-4. 1. Find the slope of the line. $-8/4$ 2. Find the $y$-intercept of the line. $4$ 3. Write an equation for the line in slope intercept form. $Y = -8/4x + 4$ 4. Which of the following equations could also be used to describe the graphed line?

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jennifer b.