0
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0answers
25 views

Soft question: Distribution of the kth powers of normal random variables.

If $X_1,..,X_n$ are standard normal random variables then it is knows that: $\underset{i=1}{\overset{n}{\sum}} X_i$ is a normal random vairable and $\underset{i=1}{\overset{n}{\sum}} X_i^2$ is a ...
1
vote
2answers
48 views

If $X$ is distributed normally with mean $0$, is it correct to say $X$ and $-X$ “have the same distribution”?

Q: If $X$ is distributed normally with mean $0$, is it correct to say $X$ and $-X$ have the same distribution? In a way, this seems correct: both $X$ and $-X$ have the same probability density ...
0
votes
0answers
10 views

Terminology for 'clusters' in a discrete probability distribution?

I have attached an image of a probability distribution. As you can see their are peaks, and in my opinion thee 'clusters' in this distribution. There is the cluster that spans the origin and goes out ...
1
vote
2answers
48 views

Proper name for the generalized binomial distribution with two trials?

Two Bernoulli trials are performed, first with success probability $p_1$ and second with success probability $p_2 \not=p_1$. The resulting distribution for the number of positive outcomes is ...
3
votes
1answer
65 views

Name/significance of integral of the square of a probability density function

Background/Motivation Given a probability density function $f(x)$, the mean of the corresponding random variable is the $x$-coordinate of the centroid of the region under the graph of $f$. I ...
0
votes
2answers
304 views

Probability of a Min/Max

I am studying probability for an exam and I am finding hard to understand the notion of $P(\min(X_1,X_2))$ and $P(\max(X_1,X_2))$, where $X$ is a discrete or a continuous variable. I have found in my ...
1
vote
2answers
89 views

What is this mathematics sub-field called?

I would love to answer another question on this site, but I am totally unfamiliar with the required technique. I mean, I don't even know the sub-field's name. The field I am looking for is one that ...
0
votes
1answer
134 views

How to describe a “sum percentile”

I have values $w_1 \ge w_2 \ge ..\ge w_n$. I want to know the the highest possible threshold $w^{th}$ so that $$ \sum_{i:w_i>w^{th}} w_i \ge \alpha \sum_{i=1}^n w_i $$ where $\alpha \in [0,1]$. ...
0
votes
2answers
74 views

What is a two point support in this lemma?

What is the terminology of two point support in this lemma?
2
votes
1answer
83 views

An almost-uniform distribution over the Naturals. Does it have a name?

I've just discovered this distribution, which is almost uniform over the naturals. Surely I'm not the first to discover it? Is it interesting? Does it have a name? $ \mathrm{P}(K = k) = \frac1k ...
2
votes
2answers
204 views

Probability distribution functions: factorization 3-way implies 2-way?

I recently asked a question about pairwise versus mutual independence (also related to this and this q). However, (1) I inadvertently used incorrect terminology: three events, A, B, C are ...
2
votes
2answers
1k views

How do I read this distribution function: $\min(X,Y)$?

I'm confused on what the $\min$ means. For example if I need to find the distribution function of $\min(X,Y)$ what am I looking for exactly? Am I looking for the distribution of the minimum value of ...
3
votes
1answer
490 views

Do hashing functions have a probability distribution calculated for their output?

This question might look strange, so I will try to be clear. Consider a hashing function $f : M \mapsto H$ which takes a message with arbitrary length $m \in M$ as input and returns a hash $h \in H$ ...
0
votes
1answer
643 views

What is the difference between FWHH and FWHM?

The title says it all really. I wanted to know if there is a situation where full width half height half maximum is more appropriate than full width half height or vice versa. Thank you
2
votes
1answer
149 views

Probability distribution explanation

What exactly is a probability distribution, and what are the two requirements for a probability distribution? I am not sure what this means or how to apply it? Any examples that can be given would ...
1
vote
1answer
109 views

Bernoulli Distribution with support different from $\{0,1\}$

Suppose the support of a distribution is $\{12 , 13 \}$ with $P(X = 12) = p$ and $P(X = 13) = 1-p$. Is this still a Bernoulli distribution even if the support is not $\{1, 0 \}$?
0
votes
1answer
344 views

doubt on iid distribution vs uniform distribution

I am a bit confused when I read "iid distribution". It looks to me like what is called "uniform distribution" i.e. a distribution of probability that is constant in a range. Am I correct in thinking ...
1
vote
1answer
98 views

Is the term Gaussian distribution the preferred term?

Is "Gaussian" the term preferred over "normal" when speaking of the distribution to which these names have been attached? Are they both referring to the same thing?
3
votes
2answers
131 views

component and dimension in Gaussian mixture model

What is the relation between a dimension and a component in a Gaussian Mixture Model? And what is the meaning of dimension and component? Thank you. Please correct me if I'm wrong: my understanding ...
20
votes
3answers
19k views

Probability density function vs. probability mass function

I've an confession to make. I've been using pdf's and pmf's without actually knowing what they are. The idea that I've been having so long is that density = area under the curve but if I look at it ...