Suppose that a utility function u represents a preference re…
Suppose that a utility function u represents a preference relation on a set X. Consider the function that assigns to each x in X, f(x)=au(x)+b, where a and b are both constants. Suppose that the preference has at least a strict ranking (the agent is not indifference between at least one pair of alternatives). Then, f represents the preference if and only if,
Read DetailsConsider a preference relation on a finite set X={x1,x2,…,xn…
Consider a preference relation on a finite set X={x1,x2,…,xn}. Suppose that it is complete and transitive. Then, the following function represents it: U(xi)= 3log|{j=1,…,n: xi at least as good as xj}|-2020, where |.| represents the cardinality of a set.
Read DetailsA coastal surveillance system uses radar to detect incoming…
A coastal surveillance system uses radar to detect incoming ships. The detection capability depends on weather conditions: Clear weather occurs 50% of the time, and the radar successfully detects ships with probability 0.95 Foggy weather occurs 30% of the time, and the radar successfully detects ships with probability 0.70 Stormy weather occurs 20% of the time, and the radar successfully detects ships with probability 0.50 What is the overall probability that an incoming ship is detected by the radar system? Keep three digits
Read DetailsIn a manufacturing facility, a batch of 50 items contains 8…
In a manufacturing facility, a batch of 50 items contains 8 defective items. Quality control randomly selects 4 items from the batch to test. The batch is accepted if at most 1 of the tested items is defective. What is the probability that all 4 tested items are non-defective? (Use combinatorics) Keep two digits.
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