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    Uses of the Probability Density Function versus the Cumulative Distribution Function

    Hi Ami44, thank you for your time. That helps to explain the inversion of function. Much clearer! Does anyone have any examples of a PDF and CDF for a discrete distribution? I think a working example would clarify. Separately, for continuous distributions: What use is a PDF? It seems like its...
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    Variance and Covariance Calculation Clarification

    Hi David, Thanks! I work in Excel every day so being able to look at the numbers was a big help. What I was describing in the first part can be summed up as: Pr*(X-µ)^2 The second equation can be described as: Pr*X^2-(sum(Pr*X))^2. sum(Pr*X) = µ What you were showing in the second example was...
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    Variance and Covariance Calculation Clarification

    As a follow-up: Var(X)=E(X^2)-[E(X)]^2 How does the above work with regards to this variance problem: A discrete uniform distribution (each event has an equal probability of occurrence) has the following possible outcomes for X: [1, 2, 3, 4]. The variance of this distribution is closest to...
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    Variance and Covariance Calculation Clarification

    Apologies in advance for any lack of precision, clearly my background is not in math. From what I read, variance is defined as two separate formulas: I believe I understand the first part of the equation: Var(X) = E[(X-u)^2] where u = E(X): (1) This means take the summation of: the actual...
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    Uses of the Probability Density Function versus the Cumulative Distribution Function

    Hi All, The probability density function seems to be a constant in most cases. As I found on Quora: A probability density function answers the question: "How common are samples at exactly this value?" I understand that the PDF in a continuous distribution would be equal to 0. It seems...
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