2. Consider the experiment of rolling a die until a "6" appears. Let X be the number of rolls needed. Plot the Cumulative distribution function Fx(x) of X. Describe what it means for a function to be right-continuous. You are encouraged to use a computer program to plot this, although it is acceptable that you use rulers and pencils. (You don't need to plot the whole function because the possible values could be ar- bitrary large. Try to plot from 0 to the value that you think it shows the major trend.)
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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