Suppose that t weeks after the start of an epidemic in a certain community, the number P(t) of people who have caught the disease is given by the logistic curve P(t) =3000 5+295e−0.3t (a) How many people had the disease when the epidemic began? (b) Approximately how many people in total will get the disease? (c) When was the disease spreading most rapidly? (d) How fast was the disease spreading at the peak of the epidemic? (e) When did the spread of the disease start to slow down? (f) What is the differential equation for P(t)? g) By the time 400 people had the disease, what was the rate at which the disease was spreading?
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!
Suppose that t weeks after the start of an epidemic in a certain community, the number P(t) of people who have caught the disease is given by the logistic curve P(t) =3000 5+295e−0.3t (a) How many people had the disease when the epidemic began? (b) Approximately how many people in total will get the disease? (c) When was the disease spreading most rapidly? (d) How fast was the disease spreading at the peak of the epidemic? (e) When did the spread of the disease start to slow down? (f) What is the differential equation for P(t)? g) By the time 400 people had the disease, what was the rate at which the disease was spreading?
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