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Still in connection with given Example, show that the posterior distribution on (a, b, c, σ - 2) is a standard distribution made of a trivariate normal on (a, b, c) conditional on σ and the data and a gamma distribution on σ -2 given the data.
Example
The cars dataset relates braking distance (y) to speed (x) in a sample of cars. Given Figure shows the data along with a fitted quadratic curve that is given by the R function lm. The model posited for this dataset is a quadratic model
yij = a + bxi + cxi2 + εij, i = 1,...,k, j = 1,...ni,
where we assume that εij ∼ N(0, σ2) and independent.
The probabilities of two events X and Y are 0.4 and o.6 respectively.- What are the conditional probabilities of X and Y occurring, given that A, B or C has already occurred?
Find the total sample size needed using a two-sided test at the 0.05 level of significance and a statistical power of 80% to detect the alternative hypothesis that the two-year relapse rates in the placebo and the new drug arms are 60% and 40%, re..
If the life of wild pheasants follows a normal distribution with a mean of 9 months and a variance of 9, what percent of the population will be less than 11 months of age?
A 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.
According to this study, the estimate for p, the proportion of all "likely voters" who will vote for the Republican candidate, is p = .601. Find a bound for the error of estimation.
consider the following minimization problemmin z x1 2x2s.t. x1 x2 3002x1 x2 4002x1 5x2 750x1 x2 0what is the
Suppose the distribution of speed at one location on a highway is bell shaped with a mean of 73 mph and a standard deviation of 4 mph. About 95% of vehicles at that location travel between
To demonstrate the effectiveness of the drug, a researcher selects a sample of n = 25 children diagnosed with the disorder and measure each child's attention span before and after taking the drug.
A small New England college has a total of 400 students.The Math SAT is required for admission, and the mean score of all 400 students is 620. The population standard deviation is found to be 60. The formula for a 95% confidence interval yields th..
Compute the Return to Risk Ratio (RRR). On the basis of the results of (A) - (C), which action should the vendor take - sell soft drinks or ice cream? Why?
If X is a normally distributed random variable with mean 97 and standard deviation 10, ?nd x2 such that P (102 X x2) = 0.05.
Estimate the mean number of cars per household for the population of households in the neighborhood. Give the 95% confidence interval.
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