continuous random variable
A continuous random variable is a type of random variable that can take on any value within a specific range
A continuous random variable is a type of random variable that can take on any value within a specific range. Unlike a discrete random variable, which can only take on specific values, a continuous random variable can assume any value over a continuous range.
Examples of continuous random variables include the height of a person, the temperature in a room, or the time it takes to complete a task. These variables can take on an infinite number of values within their respective ranges.
One characteristic of continuous random variables is that their probability distribution is described by a probability density function (PDF) rather than a probability mass function (PMF). The PDF represents the likelihood of a random variable taking on a specific value within a range. It is important to note that the actual probability of a continuous random variable taking on a specific value is zero due to the infinite number of possible values.
To calculate probabilities or perform statistical analysis with continuous random variables, we integrate the PDF over a specific range of interest. For example, to find the probability that a person’s height is between 160 cm and 180 cm, we need to calculate the integral of the PDF of the height random variable over that range.
Continuous random variables also have cumulative distribution functions (CDF), which give the probability that a random variable takes on a value less than or equal to a specific value. The CDF is obtained by integrating the PDF from negative infinity to the specific value of interest.
In summary, continuous random variables can take on any value within a specified range. Their probability distributions are described by probability density functions (PDFs) and cumulative distribution functions (CDFs) are used to calculate probabilities and perform statistical analysis with these variables.
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