2379-chapter7 - MAT 2379 Introduction to Biostatistics...

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MAT 2379, Introduction to Biostatistics, Lecture Notes for Chapter 7 1 MAT 2379, Introduction to Biostatistics Chapter 7. Continuous Random Variables 7.1 Definition Continuous random variables can assume an infinite number of values in some interval. The ma- jor mathematical difference between continuous and discrete random variables is that the probability that a continuous random variable X takes a particular value x is 0, that is: P ( X = x ) = 0 for any numerical value x. Examples of continuous random variables: 1. The weight (or height) of an individual; 2. The blood pressure (or temperature) of a patient; 3. The weight gain of a woman during pregnancy. 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 : P ( a X b ) = Z b a f ( x ) dx This can be represented graphically as the area under the graph of f between the points a and b . Moreover, since f ( x ) are probabilities, we should always have f ( x ) 0 and Z f ( x ) dx = 1
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