8. Birthdays are distributed independently and uniformly across the year which, ig- noring complications from leap years, is considered to have 365 days. What is the expected number of days that are birthdays to exactly k individuals in a given population of n individuals? Numerically evaluate your expression as k varies from 0 through 5 for each of the three cases n = Are any of the answers surprising? 10, n = 100, and n = 1000. %3D
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!
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