The probability that the majority of a three- person jury will convict a guilty person is given by the formula:P(r, s, t) = rs(1 - t) + (1 - r)st + r(1 - s)t + rst subject to the constraint thatr + s + t = a,where r, s, and t represent each of the three jury members’ probability of reaching a guilty verdict and a is some fixed constant that is generally less than or equal to the number of jurors. Source: Mathematical Social Sciences.(a) Form the Lagrange function.(b) Find the values of r, s, and t that maximize the probability of convicting a guilty person when a = 0.75.(c) Find the values of r, s, and t that maximize the probability of convicting a guilty person when a = 3.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The probability that the majority of a three- person jury will convict a guilty person is given by the formula:
P(r, s, t) = rs(1 - t) + (1 - r)st + r(1 - s)t + rst subject to the constraint that
r + s + t = a,
where r, s, and t represent each of the three jury members’ probability of reaching a guilty verdict and a is some fixed constant that is generally less than or equal to the number of jurors. Source: Mathematical Social Sciences.
(a) Form the Lagrange function.
(b) Find the values of r, s, and t that maximize the probability of convicting a guilty person when a = 0.75.
(c) Find the values of r, s, and t that maximize the probability of convicting a guilty person when a = 3.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
