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yousif1429 said:
A random variable is a numerical value that is assigned to each outcome of a random event. It can take on different values with different probabilities, and is used to represent uncertainty in a mathematical way.
Probability is used to describe the likelihood of different outcomes of a random variable. It assigns a value between 0 and 1 to each possible outcome, with 0 representing impossibility and 1 representing certainty.
Discrete random variables can only take on a finite or countably infinite number of values, while continuous random variables can take on any value within a certain range. For example, the number of heads in 10 coin tosses is a discrete random variable, while the height of a person is a continuous random variable.
The expected value of a random variable is calculated by multiplying each possible outcome by its respective probability and summing them all together. It represents the average value that we would expect to see if we repeated the random experiment many times.
The variance and standard deviation of a random variable measure the spread or variability of its values around the expected value. A smaller variance/standard deviation indicates that the values are closer to the expected value, while a larger variance/standard deviation indicates more variability.
