# Linked Questions

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 ?
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 ...
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 ...
1answer
103 views

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

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