Find a double integral that represents the exposure of a person residing at A(x0, y0). (b) Evaluate the integral for the case in which A is the center of the city and for the case in which A is located on the edge of the city. Where is the risk of infection lower? The edge of the city, or The center of the city?
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!
When studying the spread of an epidemic, we assume that the probability that an infected individual will spread the disease to an uninfected individual is a function of the distance between them. Consider a circular city of radius 41 mi in which the population is uniformly distributed. For an uninfected individual at a fixed point A(x0, y0), assume that the probability function is given, d(P, A) denotes the distance between P and A.
(b) Evaluate the integral for the case in which A is the center of the city and for the case in which A is located on the edge of the city. Where is the risk of infection lower?
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