Question Measurements for the length and width of a rectangular plastic covers for CDs are rounded to the nearest mm (so they are discrete). Let X denote the length and Y denote the width. The possible values of X are 129, 130, and 131 mm. The possible values of Y are 15 and 16 mm. The joint distribution is given by the following table: X-length 129 130 131 Y=width 15 0.12 0.42 0.06 16 0.08 0.28 0.04 The probability that a CD cover has width of 16 mm knowing that it has a length of 129 mm is: 0.13 0.4 0.08 0.2
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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