x >1 f(x) =x10 xs1 ermine the value of k for which f(x) is a legitimate pdf. ain the cumulative distribution function. x > 1 xs1 the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) ain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) n dard deviation it is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)
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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