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Let X1 depend on θ1 and X2 be independent of X1 and depend on θ2. Let θ1 and θ2 have independent prior distributions. Assume a squared-error loss. Let δ1 and δ2 be the Bayes estimators of θ1 and θ2 respectively
1) Show that δ1 - δ2 is the bayes estimator of θ1-θ2 given X = (X1, X2) and the setup described.
2) Now assume that θ2 > 0 (with probability 1), and let δ1 hat be the Bayes estimator of 1/θ2 under the setup above. Show that δ1δ2 hat is the bayes estimator of θ1/θ2 , given x = (X1, X2)
Assuming that a plane make a safe flight if at least one-half of its engines run, determine whether a 4-engine plane or 2-engine plane has the higher probability for a successful flight.
Consider the following age data, which is the result of selecting a random sample of 20 United Airlines pilots.
A "one-shot" device can be used only once; after use, the device (e.g. a nuclear weapon, space shuttle, automobile air bag) either is destroyed or must be rebuilt.
Choice of exponential smoothing constant w has little or no effect on forecast values using exponential smoothing.
The manager wants to know the probability that any particular cookie will have fewer than 5. What type of probability distribution will most likely be used to analyze the number of chocolate chips per cookie?
Compare the differences of Simple random sampling & Cluster sampling using specific examples, and show the pros and cons of each method.
Qualitative or ethnographic research uses open-ended questions that attempt to nuance the distinctions that quantitative research attempts do to numerically.
Do these data lend support to this belief? Perform a significance test to answer this question. Construct and interpret a 95% confidence interval for the difference in proportions.
Should the finite-population correction factor be used? Why or why not?
We suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in years), so we choose a random sample of drivers who have similar automobile insurance coverage and collect data about th..
Draw a simulation experiment for car agency and simulate using fleet of four rental cars for 10 days.
What is the probability that of today's 1,100 callers at least 5 received a busy signal? Use the poisson approximation to the binomial.
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