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 ?
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 ...
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 ...
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 $$df = \frac{1}{\pi}\frac{dx}{1+(x-m)^2}$$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
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 ...
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.
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 ...
### 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 ...