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khansen9
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Hey everyone, I have been struggling to find the expected value and median of f(x) = 1/2e^-x/2, for x greater than 0. I am just wondering how I do so? Thank you.
How do I find the expected value and median of a probability density function?
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- Thread starter khansen9
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In summary, Integral Expected Value is a mathematical concept used in probability theory to represent the average value of a continuous random variable over a given interval. It is different from regular Expected Value, which is used for discrete random variables. Integral Expected Value is important because it helps us make predictions and understand the behavior of a system. The formula for calculating it is E[X] = ∫x * f(x) dx, and it has various real-world applications in fields such as finance, physics, and engineering.
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ergospherical
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What are the definitions of the expectation and the median for a continuous random variable? 
- #3
mathman
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If f(x) is supposed to be a probability density, then it has to be normalized so its integral = 1.
1. What is the definition of Integral Expected Value?
Integral Expected Value is a mathematical concept used to calculate the average value of a continuous random variable over a specific interval. It takes into account all possible outcomes within that interval and assigns a weight to each outcome based on its probability of occurrence.
2. How is Integral Expected Value calculated?
To calculate Integral Expected Value, the function representing the probability distribution of the random variable is multiplied by the variable itself and integrated over the interval of interest. The result is the weighted average value of the variable over that interval.
3. What is the significance of Integral Expected Value in statistics?
Integral Expected Value is a fundamental concept in statistics as it allows us to determine the expected outcome of a continuous random variable. It is used in various statistical models and calculations, such as calculating the mean and variance of a distribution.
4. Can Integral Expected Value be negative?
Yes, Integral Expected Value can be negative. It is possible for a continuous random variable to have a negative expected value if the function representing its probability distribution has a significant portion of its area below the x-axis.
5. What are some real-life applications of Integral Expected Value?
Integral Expected Value has many practical applications, such as in finance, where it is used to calculate the expected return on investments. It is also used in risk analysis, predicting future outcomes, and in various fields of science, including physics, engineering, and biology.
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