RVCND - Continuous Random Variables Lesson

Continuous Random Variables Lesson

Our study of statistics began by discussing the shape of distributions using terms like symmetric or skewed when describing quantitative data. Continuous distributions result from smoothing out histograms that can take any shape. Some shapes are common enough that we study them as a group. One such example is a "uniform distribution." A uniform distribution is one for which the probability of occurrence is the same for all values of X. It is sometimes called a rectangular distribution. For example, if a fair die is thrown, the probability of obtaining any one of the six possible outcomes is 1/6. Since all outcomes are equally probable, the distribution is uniform. A uniform distribution has no clear peaks.

The probability model for a continuous random variable assigns probabilities to intervals of outcomes rather than to individual outcomes.   In fact all continuous probability distributions assign probability 0 to every individual outcome. Only intervals of values have positive probability.   Calculations are straightforward when working with uniform distributions.   The probability will be the area under the curve (graph) between the endpoints.   You may be able to tell that this use of area of intervals could be related to calculus.   

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