Linked Questions

3
votes
0answers
3k 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
0answers
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 ...
0
votes
0answers
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. ...
41
votes
4answers
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.
23
votes
6answers
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?
18
votes
2answers
3k views

Why is the Cauchy Distribution so useful?

Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
17
votes
3answers
8k views

Does non-zero correlation imply dependence?

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 $...
9
votes
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 ...
7
votes
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 \...
3
votes
1answer
23k 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 ...
9
votes
1answer
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[(...
5
votes
1answer
7k views

When does a distribution not have a mean or a variance?

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 ...
7
votes
1answer
4k views

What are the mean and variance of the ratio of two normal variables, with non-zero means?

If X,Y are normal independent N(a,s), N(b,s') what are means and variances of the ratio X/Y ?
8
votes
2answers
768 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 ...
3
votes
3answers
391 views

Where does the expected value definition come from? [duplicate]

The definition of the expected value on the domain $[a,b]$ is given by $$E[X] := \int_a^b x f(x) \, \mathrm dx $$ I understand what the mean is, but I don't fully understand how this specific equation ...

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