What Continuous random variable is
A continuous random variable is a type of random variable that can take on any value within a given range. Continuous random variables are usually used to model real-world phenomena such as the height or weight of a person, the temperature or pressure of a gas, or the speed of a car.
Steps for Continuous Random Variable:
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Define the range of values the random variable can take on. These values should be continuous, meaning that the values should be spread out over a range and not be a finite set of numbers.
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Determine the probability distribution for the random variable. This is typically done by finding the probability density function (PDF) or the cumulative distribution function (CDF) of the random variable.
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Calculate the expected value, or mean, of the random variable. This is done by integrating the PDF or CDF of the random variable.
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Calculate the variance of the random variable. This is done by integrating the squared PDF or CDF of the random variable.
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Calculate any other characteristics of the random variable that may be of interest, such as the skewness or kurtosis.
Examples
- The time it takes for a light bulb to burn out.
- The length of a phone call.
- The age of a person.
- The time it takes for a website to load.
- The amount of rainfall in a given area over a period of time.
- The amount of time it takes for a train to travel a certain distance.
- The number of cars driving on a highway in a given hour.
- The number of emails received in a given day.