Over time, the number of original basicwords in a language tends to decrease as words becomeobsolete or are replaced with new words. In 1950, C. Feng andM. Swadesh established that of the original 210 basic ancientChinese words from 950 a.d., 167 were still being used. Theproportion of words that remain after t millennia is a randomvariable that is exponentially distributed with a = 0.229.Source: The UMAP Journal.a. Find the life expectancy and standard deviation of aChinese word.b. Calculate the probability that a randomly chosen Chineseword will remain after 2000 years.
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!
Over time, the number of original basic
words in a language tends to decrease as words become
obsolete or are replaced with new words. In 1950, C. Feng and
M. Swadesh established that of the original 210 basic ancient
Chinese words from 950 a.d., 167 were still being used. The
proportion of words that remain after t millennia is a random
variable that is exponentially distributed with a = 0.229.
Source: The UMAP Journal.
a. Find the life expectancy and standard deviation of a
Chinese word.
b. Calculate the probability that a randomly chosen Chinese
word will remain after 2000 years.
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