New answers tagged random-variable
1
vote
Bounding the distance of empirical average from its expected value
This appears to be impossible without extra assumptions.
To illustrate, take $\nu_a = 0$, $\nu_c = 1$. Then $(X_n)$ is a totally unconstrained sequence of random variables: considering $1_{[X_1 = b]} \...
- 23.7k
4
votes
Does it make sense to model population distributions as independent from individual distributions? (social sciences)
Population distributions are different to distributions of individual values, but they can be closely related (e.g., in the IID model)
I will give you a run-down of how this is usually treated in ...
- 116k
0
votes
Accepted
Calculation of multivariate probability mass function
The start of your solution looks correct to me. We have
$$
\begin{align}
p & = P(X_1-X = n, \ldots , X_{N-1}-X = n ) \\
& =
\sum_{i=1}^\infty P(X_1-X = n, \ldots , X_{N-1}-X = n | X = i) P(X =...
- 2,088
0
votes
Does it make sense to model population distributions as independent from individual distributions? (social sciences)
does it make sense to think of populations having separable paremeters/moments/distributions from individual ones,
The distribution of a population describes the variations that occur in the ...
- 68.3k
0
votes
How is this Negative Binomial Random variable used to solve this problem?
The trick here is that the binomial coefficient has a symmetry property that allows it to be written in two equivalent ways. In this case, the relevant symmetry is that:
$${n-1 \choose r-1} = {n-1 \...
- 116k
6
votes
Accepted
What affects correlation in this situation?
I would have said a sample of $20$ observations rather than $20$ samples.
Suppose the four states are the four visible clusters in this scatterplot:
In each state separately there is zero correlation,...
- 8,511
2
votes
What affects correlation in this situation?
Don't think about "significant" vs. "not significant" (see Andrew Gelman's paper "The Difference between "Significant" and "not Significant" is not, itself,...
- 104k
6
votes
Accepted
Distribution of a sum of linear combinations of random variables, each drawn from a set of random variables
First, note that
$$
\begin{align}
Z&=\sum_{k=1}^m Y_k
\\&= \sum_{k=1}^m\sum_{i=1}^n w_{i,k}X_i
\\&= \sum_{i=1}^n(\sum_{k=1}^m w_{i,k})X_i
\\&= \sum_{i=1}^n w_i X_i
\\&=\mathbf{w}^...
- 10.4k
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