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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 ...
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### 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. ...
31k 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.
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### 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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We know of the fact that zero correlation does not imply independence. I am interested in whether a non-zero correlation implies dependence - i.e. if $\text{Corr}(X,Y)\ne0$ for some random variables $... 4answers 14k views ### How does the expected value relate to mean, median, etc. in a non-normal distribution? How does the expected value of a continuous random variable relate to its arithmetic mean, median, etc. in a non-normal distribution (eg. skew-normal)? I'm interested in any common/interesting ... 2answers 2k views ### WLLN: can expectation exist but be infinite? Weak law of large numbers: Let$\{h_i, i = 1, \dots n\}$be an$m \times q$sequence of iid random variables with mean$\mu = E[h_i]$that exists and is finite. Then$1/n \sum_{i = 1}^n h_i \...
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 ...