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    Estimated standard error

    Why is it ok to estimate the population variance with the sample variance formula (i.e. the unbiased estimate of the variance). I understand how we can build a confidence interval using the central limit theorem and the following formula . But, the unbiased estimate of the variance means that...
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    Modified population variance

    I don't understand the term "modified population variance" used in this pdf file:///C:/Users/marya/AppData/Local/Packages/Microsoft.MicrosoftEdge_8wekyb3d8bbwe/TempState/Downloads/RSbook_ch3%20(1).pdf. Is it related to the concept of unbiased estimator of the population variance? Also, why do...
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    Change of variable

    Let's say f(x)=ax+c. Is g(x)=f(x)+d called a "change of variable"?
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    Change of variable

    Consider the function y=ax +b. The term "change of variable" is used for inside changes, i.e. changes that affect the input ( x-) axis values. Can the term "change of variable" be used for changes that affect the output ( y-) axis values?
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    Distribution invariant under transformation

    On the page on relationships among probability distributions on Wikipedia there is a line saying that "some distributions are invariant under a specific transformation". Could anyone explain what it means please.
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    data transformation

    If Y=log(X) is normally distributed, then X is lognormally distributed. Does this mean that if I plot the probability density function of Y, the x-axis is log(x)?
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    Generating a uniform function from an exponential function

    Thank you GretaGarbo and Dason. Now I can describe what the transform does with words and graphs. However, I am still confused when it comes to the formulas, especially the x's. The formula for the CDF is and putting X into this gives . So, if I have a dataset (x1, x2,...,x50) and I put them...
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    Generating a uniform function from an exponential function

    I'm sorry I don't understand. I know you are right but I don't get why we get a uniform. If I put x's were the x is in the CDF, shouldn't I get a CDF? (I'm sorry if I am not very clear, I'm very confused and I really appreciate your help!)
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    Generating a uniform function from an exponential function

    If I have some values x. From these I estimate the PDF of an exponential function f(x)= . Let's say the estimated lambda equals 50. The CDF is . How do I generate a standard uniform distribution from this?
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    data tranformation

    Sorry for removing the question. I have posted it again.
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    data tranformation

    How do I interpret this notation? If QN(p) is the normal quantile function, then F(Y)= QN[G(Y)] follows a normal for any G ∼ G(Y)
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    Degrees of freedom and sampling with replacement

    The modified population variance (divisor n-1) can be explained by degrees of freedom. The mean is fixed so specifying the value of any n-1 determines the remaining value. I understand how this applies to sampling without replacement. Why doesn't this apply to sampling with replacement from a...
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    Inverse of CDF

    I am so thankful! That is exactly what I needed to get my head around the notation. Thank you very much!!
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    Inverse of CDF

    I am struggling to understand the second formula. I understand the first formula. I don't understand why F(x) is greater than or equal to y in the second formula. Shouldn't the sign be similar to the first formula?
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  16. M

    MMSE vs LSE

    title without abbreviations: minimum squared error, ordinary least square, minimum mean square, least square, mean squared I am trying to understand methods for point estimation and their hierarchy in an applied perspective I understand the concept of least squared error. I understand that...
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    Defintion of a random variable

    Thank you Dason and hlsmith!
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    Interpretation of inverse CDF

    For the PDF above what is the inverse CDF of 0 and 0.75, i.e. Q(0) and Q(0.75)?
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    Defintion of a random variable

    I have read two defintions for a random variable. 1. It is a function from the set of all posisible outcomes to the real line. For example Y("male")=0 2. A variable where known probabilities are associated with sample outcomes. Which one is correct? Defintion 1 does not include a probability...
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    Support vs sample space

    I understand that the term support is not used in the same sense in mathamtics and statistics. However, I cannot really understand difference between support and sample space when it comes to statistics. Could you say that the support isa subset of the sample space, i.e. all sample points that...