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The marginal likelihood is the resulting pmf/pdf after integrating out (marginalzing) the pa- rameters #. It can understood as the expected likelihood with respect to the prior p(0). It is given by p(y) = JOEe p(y | 0 )p(0)de = Epco) {p(y | 0) }. When e is a vector this will be a multidimensional integral, and in some cases it can be REALLY hard to obtain. Notice that this is the denominator of the posterior density, which is why it so convenient being able to work with the posterior up to proportionality. Example 2. Marginal obtained from the Beta-Bernoulli model As in the coin-flipping problem, if 0 ~ Beta(a, b) and Y1, ..., Y, are iid Bernoulli(@), then the marginal likelihood is given by p(y) = p(yl:n) = Jace p(y1:n | 0)p(@) de BEvi(1 - 0)"-Evi JOEO B(a, b) "-(1 -p)b-'de B(a+ Cyi, b+ n - >yi) = B(a, b)Use the given frequency distribution to find the Temperature (OF) Frequency (a) class width. 50-52 (b) class midpoints. 53-55 (c) class boundaries. 56-58 59-61 62-64 65-67 68-70 (a) What is the class width? (Type an integer or a decimal.) (b) What are the class midpoints? Complete the table below. (Type integers or decimals.) Temperature (OF) Frequency Midpoint 50-52 53-55 u W 56-58 59-61 11 62-64 65-67 68-70 O (c) What are the class boundaries? Complete the table below. (Type integers or decimals.) Temperature ('F) Frequency Class boundaries 50-52 53-55 in W 56-58 59-61 11 62-64 65-67 68-70 OApps He Blackboard Learn Drive Safely Y Acid and bases in Of MyMathLab Andrew Aguirre Quiz: Unit 2 CA: Descriptive Statistics Quiz Time Limit: 00:50:00 Subm This Question: 3 pts 2 of 10 (1 complete) This Quiz: 30 pts Use the frequency distribution shown below to construct an expanded frequency distribution. High Temperatures ("F) Class 18-28 29-39 40-50 51-61 62-72 73-83 84-94 0 Frequency, f 18 43 66 67 84 66 21 18-28 18 29-39 43 40-50 66 51-61 67 62-72 84 73-83 66 Enter your answer in each of the answer boxes. 4 GOODiFWOPXOL