MAT 2379 Lecture Notes - Lecture 5: Standard Deviation, Probability Distribution, Random Variable
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Up to now we have been working with discrete random variables whose range is finite or countable. However we will have to allow for variables that can take values an interval of real numbers. The weight (or height) of an individual; 2. The blood pressure (or temperature) of a patient; 3. A random variable x is said to be continuous if its cumulative distribution function f is a continuous function. As in the discrete case, the cumulative distribution function f(x0) gives the probability that x takes values smaller or equal to x0: where f(x) is the probability density function of x. 0, otherwise, where f 0 is the derivative of f. For continuous random variables, the best thing that one can do is to estimate the probability that the variable will take values in a given interval [a,b]. The function f which gives these probabilities is called the density function of x: