1. ### 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...
2. ### 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...
3. ### Change of variable

Let's say f(x)=ax+c. Is g(x)=f(x)+d called a "change of variable"?
4. ### 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?
5. ### 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.
6. ### 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)?
7. ### 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...
8. ### 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!)
9. ### 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?
10. ### data tranformation

Sorry for removing the question. I have posted it again.
11. ### 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)
12. ### 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...
13. ### Inverse of CDF

I am so thankful! That is exactly what I needed to get my head around the notation. Thank you very much!!
14. ### 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?

deleted