Linked Questions

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 ?
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 ...
4
votes
1answer
724 views

When can't a confidence interval be constructed?

In one of my econometrics assignments, we were asked to consider the effect of measurement error in the dependent variable of a simple linear regression. And I was just wondering, under what ...
4
votes
1answer
103 views

Fisher's example of a non-converging mean for N towards infinity

In one of Fisher's classical paper [1] I stumbled over the following: If the frequency with which the variate $x$ falls into the range $dx$, be given by $$df = \frac{1}{\pi}\frac{dx}{1+(x-m)^2}$$ ...
3
votes
1answer
24k 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 ...
2
votes
1answer
831 views

Does the k-th moment exists when $E[X^k]$ is infinite in ether (one) positive or negative direction? [duplicate]

I'm reading Probability and Statistics by DeGroot and Schervish, and in it it said that the expectation of a random variable exists if at least one of the integrals over all negative/positive values ...
1
vote
1answer
116 views

Why do I get worse regression metrics when I add more instances to the problem?

I find this counter-intuitive. First I chose randomly 7000 instances and my model explains 55% of the variance. Then I train with the whole dataset (43000) and I get negative $R^2$. How is this even ...
1
vote
1answer
114 views

Population vs sample

When we think of linear regression, the implicit assumption is that we only observe a small fraction of a possibly infinite large population. Thinking of simple averages, imagine a fair die. The ...
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 ...
2
votes
0answers
58 views

A question regarding symmetry properties of a uniform distribution [duplicate]

Was anyone able to explain why $$E(U_2) = 0$$ I don't quite understand what the relevance of the underlined statement - "by the symmetry of $U_1$" in determining $E(U_2)$ is edit: I get it now, ...
0
votes
0answers
22 views

Why Cauchy distribution has no Moment-generating Function? [duplicate]

I'm reading Casella and Berger's book. In chapter 5, they show that we can recover the distribution of the sample mean by using the following relationship between the MGF of the underlying random ...
0
votes
0answers
33 views

Proof that ratio of normal distributions is Cauchy [duplicate]

I recall that the ratio of 2 independent standard normal random variables follows a Cauchy distribution, but I don't recall if there is a proof for this.
0
votes
0answers
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 ...
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. ...

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