Linear transformations of a random variable involve multiplying or adding constants to the original random variable. This changes the scale and location of the distribution, but does not change its shape.
Think of a linear transformation as resizing and shifting a picture on your phone. You can make it bigger or smaller by multiplying it with a constant, and you can move it around by adding or subtracting values. The content remains the same, but its appearance changes.
Expected Value: The expected value is the average value that we would expect to get if we repeated an experiment many times. It represents the center of mass for a probability distribution.
Variance: Variance measures how spread out the values of a random variable are from their mean. It quantifies the variability or dispersion in the data.
Covariance: Covariance measures how two random variables vary together. It indicates whether they have a positive or negative relationship, or if they are independent.
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