Linked Questions

5
votes
1answer
187 views

Is it possible for an expected value not to exist? [duplicate]

A probability density family for $x\in\mathbb{R}$ is $$f(x) = k(\theta)\left[1 + (x/\theta)^2\right]^{-1}$$ parameterized by $\theta \gt 0$. I am supposed to find $k(\theta)$ and then both $E(X)$ ...
0
votes
0answers
477 views

Finite Mean and Finite Variance [duplicate]

Let $X$ be a random variable. Suppose there exists a constant $c ∈ R$ such that $E(|X − c|^2) < ∞$. Show that the random variable $X$ has finite mean and variance. And I'm quite confused about the ...
3
votes
2answers
68 views

What happens when you try to find standard deviation of a (non-truncated) cauchy distribution? [duplicate]

I have read that this doesn't work, but I do not understand exactly why. Please can someone explain.
0
votes
1answer
60 views

Does expected value of square of a random variable always exist? [duplicate]

Can we verify if $E(X^2)$ also exist, provided that E(X) exists? Thanks.
3
votes
0answers
33 views

Can the variance of a continuous random variable with known distribution be impossible to find? [duplicate]

I am solving a problem where the life expectancy of a microorganism can be modeled as having the PDF: $ f(x)= \left\{ \begin{array}{ll} kx^{-3} & x\geq 1 \\ 0 & x \lt 1 \\ \end{...
1
vote
0answers
27 views

Random variable with finite exponential first moment, infinite exponential variance [duplicate]

Could you provide an example of a random variable $X$ such that $\mathbb{E}(e^X)<\infty$ but $\text{Var}(e^X)=\infty$? Related: "Random variable with finite logarithmic first moment, infinite ...
1
vote
0answers
18 views

Random variable with finite logarithmic first moment, infinite logarithmic variance [duplicate]

Could you provide an example of a random variable $X$ such that $|\mathbb{E}(\ln(X))|<\infty$ but $\text{Var}(\ln(X))=\infty$, if such a random variable exists at all? Related: "Random ...
43
votes
4answers
35k 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.
20
votes
1answer
7k views

Cauchy Distribution and Central Limit Theorem

In order for the CLT to hold we need the distribution we wish to approximate to have mean $\mu$ and finite variance $\sigma^2$. Would it be true to say that for the case of the Cauchy distribution, ...
5
votes
1answer
8k 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 ...
4
votes
1answer
225 views

Is it possible for a distribution to have infinite variance but finite covariance or vice versa?

Is it possible to have distributions s.t. one/both have infinite variance, but finite covariance? What about finite variance but infinite covariance? If so, what are example distributions/what is the ...
3
votes
1answer
202 views

If $X < a$, $EX < a$?

If a r.v. $X < a$, does it imply $EX < a$? If not, why is it different from what I know: If a r.v. $X \leq a$, it implies $EX \leq a$, proved by replacing $X$ with $a$ as the integrand. Note ...
0
votes
0answers
168 views

How to calculate the variance of the Item Count Technique (aka Unmatched Count Technique) double list?

The Item Count Technique (ITC) (aka Unmatched Count Technique) is a survey technique to ask a sensitive question while taking account to the anonymity of the respondent's answer. Therefore in standard ...
0
votes
1answer
29 views

For a time series, does finite variance imply finite autocovariance?

If variance is finite at all times, does this imply that all pairwise autocovariances are also finite?
1
vote
0answers
24 views

How do we determine if the true population distribution has a finite mean and/or variance? [duplicate]

Some distributions do not have finite/defined mean/variance: How can a distribution have infinite mean and variance? Is there a way to determine from your sample if the population distribution has ...