# Lecture_05 - 1 ISE 690 Statistical Methods for Engineers...

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1 Industrial and Systems and Engineering Management Department Fall 15 Dilcu Helvaci Barnes (Email: ISE 690 Statistical Methods for Engineers Continuous Random Variable

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2 Continuous Random Variables In contrast to discrete random variables, continuous random variables can assume an uncountable number of values. Consider the length of a pen barrel. At first glance, it appears to be about 6 in. long. If we measure it with a ruler, we may discover that it is approximately 5.75 in. long. If we send it to an appropriate lab, we may discover that it is approximately 5.7443286 in. long. Ultimately, however, we shall never exactly know it is true specific length.
3 Continuous Random Variables A continuous random variable is one which takes values in an uncountable set. They are used to measure physical characteristics such as height, weight, time, volume, position, etc... Examples 1. Let Y be the height of a person (a real number). 2. Let X be the volume of juice in a can. 3. Let Y be the waiting time until the next person arrives at the server.

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4 Continuous Random Variables Let Y be a random variable that is measured over a continuum, and let y be a specific value. If Y is truly continuous, then we can show that P(Y=y)=0. As a result, it is really does not make sense to talk about P(Y=y) for continuous random variables. Instead we talk about probabilities that the random variable falls within some interval. For example, . Let Y be a random variable. Y is said to be a continuous random variable if, at least theoretically, Y can assume any possible real value over some interval.
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• Fall '15
• DilcuBarnes
• Probability distribution, Probability theory, probability density function, Cumulative distribution function, CDF

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