# Linked Questions

4 votes
0 answers
4k views

### 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 ...
0 votes
0 answers
96 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 ...
0 votes
0 answers
53 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. ...
• 106
49 votes
4 answers
44k 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.
24 votes
6 answers
10k 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?
21 votes
2 answers
6k views

### Why is the Cauchy Distribution so useful?

Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
25 votes
3 answers
12k views

• 615
7 votes
2 answers
2k views

I'm comparing the following 4 estimators of location of the Cauchy distribution: Let $x_{1},..x_{n}$ be observations and $l$ be the log likelihood function. $x=median(x_{1},..x_{n})$, $y=x+\frac{l'(x)... • 351 10 votes 2 answers 1k views ### Bayesian lighthouse location estimation I am trying to learn Stan in R and as a fun challenge I am trying to estimate the location of a lighthouse based on the observed flashes. But the models I tried do not converge (Rhat != 1) or have ... • 2,086 3 votes 1 answer 28k views ### What is the Mean and Standard Deviation of the division of two random variables? [duplicate] I have two normally-distributed independent random variables X and Y and I need to calculate its division Z. As far as I understand the mean of Z is$\mu_Z = \frac{\mu_X}{\mu_Y}$, but I don't know ... • 31 7 votes 1 answer 11k views ### When does a distribution not have a mean or a variance? [duplicate] I believe I read today a phrase which went something like this: If a distribution has a mean and a variance ... So I guess that means some distributions do not have means or variances? I fiend ... • 2,045 10 votes 1 answer 3k views ### Central Moments of Symmetric Distributions I am trying to show that the central moment of a symmetric distribution: $${\bf f}_x{\bf (a+x)} = {\bf f}_x{\bf(a-x)}$$ is zero for odd numbers. So for instance the third central moment$${\bf E[(... • 101 5 votes 2 answers 1k views ### When does the sum of two$t$-distributed random variables follow a$t$distribution? In the scope of a project, I need to find the sum of two independent$t$-distributions. I know that in the general case, the sum of two$t$-distributed random variables is not$t\$-distributed. However,...
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