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Let G = (V, E) be an undirected graph with V = {1, . . . , K}. Let C1, . . . , CL be the set of maximal cliques in G. Let p(x) = (1/Z)*exp [Sum_l=1toL(ψ_l(x_Cl))] Show that if A, B, C ⊂ V are disjoint, and if C separates A from B, (all paths from A to B go through C) then X_A, X_B are conditionally independent given X_C .
1) A random sample of customer order totals with an average of $78.25 and a population standard deviation of $22.50. Calculate a 90% confidence interval fro the mean, given a sample size of 75 orders
A package contains 18 candy canes, 13 of which are cracked. If 4 are selected, find the probability of getting exactly four cracked candy canes.
Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.05 with 95% confidence using the large-sample method.
Consider the situations and comment on whether the sample results might cause concern about the quality of the process.
What is the probability that the two selected candies are the same flavour?
A business man must travel to five different destinations
Find the test statistic and do the two-sample test for equality of proportions. Is the decision close?
The population mean is within $50.00 of the sample mean?
What test or tests would you use to rule out chance from causing the apparent differences in these data and is there a significant correlation?
Valid Confidence Interval: A pollster for the Gallup Organization randomly generates the last two digits of telephone numbers to be called, so the numbers from 00 to 99 are all equally likely. Can the methods of this section be used to constru..
Recorded the time in seconds it took for 8 participants to solve a puzzle. These times appear below. However, when the data was entered into the statistical program, the score that was supposed to be 22.1 was entered as 21.2. You had calculate..
The HR department at a certain company was asked to develop a financial planning model that would help employees address how much their portfolios would be worth in 10 years, 20 years, and when they retire. John was asked to lead this effort a..
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