ioe265f11-Lec09 - Lec 09 Continuous Random Variables Topics...

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Lec 09 –Continuous Random Variables IOE 265 F11 1 1 Continuous Random Variables 2 Topics I. Continuous Random variables II. Probability distributions for continuous random variables III. Expected values of continuous random variables
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Lec 09 –Continuous Random Variables IOE 265 F11 2 3 I. Continuous Random Variables Definition: A random variable (rv) X is said to be continuous if its set of possible values is an entire interval of numbers. Example: suppose X is an rv representing all values for a diameter between 15 and 20 mm. Or, X could be defined as 15 <= X <= 20 4 Continuous Vs. Discrete Key issue: if units for X can be subdivided to any extent continuous; if not discrete Money - ? Height – ? Practical uses – Although many continuous variables have limitations in the extent in which they may be measured (precision of measuring instrument), we prefer to treat them as continuous. Similarly, some discrete variables also may be treated as continuous. Why? continuous variables often are easier to manipulate.
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