Suppose we have the following data on the number of car crashes each month for the year 2020 in the US: Month Number of Accidents Number of Days/Month January 1735 31 February 1657 28 March 1812 31 April 1962 30 May 1965 31 June 1849 30 July 1755 31 August 1892 31 September 1796 30 October 1900 31 November 1846 30 December 1727 31 Is there any evidence that the accident rate varies seasonally, or are the data consistent with the hypothesis that the rate is constant? Hint: Under the latter hypothesis, model the number of accidents cach month as a Multi- nomial random variable with the appropriate probabilities and conduct a goodness-of-fit test. Look at the signs of the deviations, Oi - Ei, and see if there is a pattern.
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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