Suppose the number of radioactive decays is a Poisson random variable with an average rate of independent decays equal to 2 per minute. If it is now 4:20, find the following probabilities. (Answer with expressions, not numerical values: e.g. 10? e 7! instead of the numerical value 1249.291) e. It's at least 5 minutes before the next decay is observed. f. There are no decays between 6:30 and 6:45 and then there are 3 decays between 6:45 and 6:50 g. 4 decays are observed between 6:40 and 6:50 given that none occurred between 6:30 and 6:40
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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