Numerade

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Consider the N-N model with known variance, $y_1, \dots, y_n | \theta, \sigma^2 \sim N(\theta, \sigma^2)$ $\theta \sim N(\mu_0, \varphi_0^2)$ Where the hyperparameters are known. Determine the posterior distribution of $\theta$, and show that the posterior mean of $\theta$ is a weighted average between the prior mean $\mu_0$ and the sample mean $\bar{y}$ (The procedure for finding the posterior distribution is the same as that used for the beta-binomial model).

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To be binding, a price ceiling must be set at a price: Group of answer choices lower than the equilibrium price and at which quantity demanded exceeds quantity supplied. at which quantity demanded exceeds quantity supplied. lower than the equilibrium price. higher than the equilibrium price.

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1. (8 points) Let L be a regular language. Define L' = {xay ? ?* | xy ? L, a ? ?}. We take the strings in L, and add exactly one symbol anywhere in the string for anywhere it could be placed, even possibly at the beginning or end. Prove that if L is regular, then so is L'. 2. (8 points) Prove that \{0$^m$1$^n$ | $m \ge n$\} is not regular. 3. (8 points) Give a CFG for valid regular expressions over the alphabet ? = {a,b}. The alphabet of your grammar should be over {a, b, (, ), U, *, ?, ?}. You may insert more parenthesis than necessary. Here we shall use ? to represent the base-case regular expression symbolizing the set only containing the empty string, that is, ? = {?}. Use the symbol ? not as part of the regular expression, but if necessary, as part of the right-hand-side of productions of the grammar to satisfy (V??)*. You must generate all syntactically valid regular expressions.

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Question 3 Which of the following is NOT true? A. Lymphocytes are considered granulocytes. B. Basophils are considered granulocytes. C. The right lymphatic duct empties into the superior vena cava. D. B and C E. A and C

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5. Let X₁,..., Xn be IID N(u, σ^2) RV's, with σ known. Consider the hypotheses H₁: μ = μ₁, H₀: μ = μ₀ (a) Suppose H₀ is rejected by a test statistic at level α. Show that μ₀ lies outside the (1- α)-CI for μ based on X̄. (b) In (a), if

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Johanna walks into class 15 minutes late. Because of the fundamental attribution error, the professor is most likely to make what type of attribution about Johanna's behavior? O Johanna must have had an unexpected situation that causes her to be late O Johanna is low in conscientiousness O Johanna is high in conscientiousness

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7) Show how ANY TWO of the four compounds shown below could be made from the specified starting material. For each answer you must include full mechanistic detail along with any additional reagents and conditions for each synthesis: [2 x 5 marks] From Ethyl acetoacetate i) From Diethyl malonate i) ii)

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36. A preschooler spent 2 hours on the playground, 1 hour doing arts and crafts, and 2(1)/(2) hours nanning. What nercentage of her time was snent nanning?

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3. Mike owes James the following obligations: I. P10,000 due at the end of 4 years II. P1,500 due at the end of 6 years with accumulated interest from today at (0.06, m = 2) Mike will be allowed to replace his total obligation by a payment at P2,000 at the end of 2 years and a second payment at the end of 5 years, with money worth 5%. a) Find the unknown payment. Comparison date: at the end of 5 years. b) Mike wishes to replace the obligations by a first payment at the end of 2 years and twice as much at the end of 6 years with money worth 2 1/2%. Find the unknown payments at a comparison date at the end of 5 years.

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Find the curvature of the curve $ \vec{r}(t) = (-2 + 2t, 2 - 5t, -3 + 3t) $ at the point $ t = -3 $.

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alicia d.