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why is the variance of t-distribution with 1 and 2 degrees of freedom undefined while these distributions can be drawn? [duplicate]

The variance of a t-distribution is given by df/(df-2), hence the t-distribution with 1 and 2 degrees of freedom have no defined variance. Yet these distributions do exist and can be drawn, so one ...
53 views

Expected value $=\infty$? [duplicate]

If we let $U_1, U_2, U_3,..., U_n$ be uniform (0,1), find $$\mathbb E[\sum_{i=0}^n iU_i^{i-1}]$$which, using the linearity of expectation, gives $$\sum_{i=0}^n \mathbb E[i U_i^{i-1}]$$ Doing this ...
49 views

Does expectation of a r.v. always converge? [duplicate]

Let X be a random variable. Will its expectation E[X] expressed as a (possibly infinite) sum converge for arbitrary X? My intuition would be yes. Since E[X] is a function of a r.v., E[X] is a r.v. ...
32k views

What is the difference between finite and infinite variance

What is the difference between finite and infinite variance ? My stats knowledge is rather basic; Wikipedia / Google wasn't much help here.
7k views

What makes the mean of some distributions undefined?

Many PDFs range from minus to positive infinity, yet some means are defined and some are not. What common trait makes some computable?
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Why is the Cauchy Distribution so useful?

Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
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What is the Mean and Standard Deviation of the division of two random variables? [duplicate]

I have two normally-distributed independent random variables X and Y and I need to calculate its division Z. As far as I understand the mean of Z is $\mu_Z = \frac{\mu_X}{\mu_Y}$, but I don't know ...
807 views

Bayesian lighthouse location estimation

I am trying to learn Stan in R and as a fun challenge I am trying to estimate the location of a lighthouse based on the observed flashes. But the models I tried do not converge (Rhat != 1) or have ...
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49 views

A practical example where maximum likelihood correctly estimates an underlying parameter, but where least squares would fail?

Forgive my very limited understanding. I am trying to learn about maximum likelihood estimation, and how it differs from least-squares estimation. From reading a little, I understand that the two are ...