- #1
cdux
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I probably miss something basic, unless it's an abstract definition.
For a continuous random variable, the probability of any single point or value occurring is infinitesimally small. This means that the probability of the random variable taking on a specific value is essentially 0. In other words, the probability of any specific point on the real number line is equal to 0, resulting in a cumulative probability of 0 for all values on the real number line.
No, the probability of a continuous random variable cannot be greater than 0 for any single point or value. This is due to the nature of continuous random variables, which have an infinite number of possible outcomes. As a result, the probability of any single outcome is infinitesimally small, approaching 0.
The probability of a continuous random variable is calculated by finding the area under the probability density function (PDF) curve. This is also known as the integral of the PDF over a given interval. The total area under the curve is equal to 1, representing the total probability of all possible outcomes.
Understanding that the probability of a continuous random variable taking on any specific value is 0 is important for interpreting and analyzing data. It allows us to calculate the probability of a range of values, rather than a single point. Additionally, it helps us understand the concept of continuous probability distributions and their properties.
There are some cases where the probability of a continuous random variable taking on a specific value may not be exactly 0. For example, if the continuous random variable follows a discrete distribution, the probability of specific values may be non-zero. However, in general, the probability of a continuous random variable taking on any single point or value is considered to be 0.