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Question 1 - Suppose we have n independent observations from
P(y|θ) = θ/y2, y > θ, and θ > 0
(a) Find a conjugate prior distribution for θ.
(b) Find the posterior mean and variance for θ.
(c) Suppose n = 3 and observations are 2; 5 and 7. Using simulation, find the posterior mean and variance for θ and compare your results with (b).
(d) Using simulation and the observations in (c), find a 95% credible set for θ.
Question 2 - Suppose that your prior for θ is a ¼ to ¾ for a mixture of N(0, 1) and N(1, 1) and that a single observation y∼N(θ, 1) turns out to equal 3. What is your posterior probability θ > 2?
two minor league baseball players got a total of 390 hits. Washington had 2 more hits than sanchez find the number of hits for each player.
Last season a major league baseball player got 120 hits in 240 times at bat. If the player expects to bat 500 times in the entire season with the same ratio of hits to at bats, how many hits can the player expect to have?
Find the length of the sides parallel to the store and perpendicular that will maximize the total area of the outdoor enclosure.
If the merchant samples the fruit, what are the probabilities of accepting a Good box, accepting a Bad box, and not accepting the box? What are these probabilities if he does not sample the fruit
SPREAD OF A CONTAGIOUS DISEASE The incidence (number of new cases/day) of a contagious disease spreading in a population of M people is given.
We also discussed rotations of common shapes in the plane using a change-of-base. Walk through one or two examples and discuss how the "usual" basis {(1,0) and (0,1)} can be limiting. Does this suggest why other bases might be better in certain ci..
Calculate the sample proportion, µ for the proportion of offspring peas with yellow pods.
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find whether the given function is linear function or not.for each of the relationships below explain whether you think
complete assignment with
Why is the concept of acculturation important to marketers who want to target such groups as Hispanic, Asian or African American consumers?
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