Linked Questions
29 questions linked to/from Can anyone clarify the concept of a "sum of random variables"
2
votes
0
answers
347
views
Sum of Discrete Random Variables [duplicate]
If I have two independent discrete random variables, say,
$$ X \in \{1,3,10,20\} $$
and
$$ Y \in \{2,3,5,9,11,15\} $$
and let $$Z = X + Y $$
be the sum of two variables. Also, each value taken by ...
- 253
0
votes
0
answers
40
views
When do we say a variable is Normally distributed? [duplicate]
Going back to the basics for a second. Say we have a random variable Y that is normally distributed: $X$~$N(\mu_1,\sigma_1^2)$. That means the pdf of X is: $$f_X(x)=\frac{1}{\sqrt{2\pi}\sigma_1}e^{-\...
- 4,792
0
votes
0
answers
34
views
Calculate $ E(Y) $ when $ Y = max(X, 2\theta - X ) $ [duplicate]
Calculate $ E(Y) $ when $ Y = max(X, 2\theta - X ) $ when $ X $ ~ $ Uniform U( 0 , 2\theta ) . $
To this question, one of my classmates answered like this
Let $ A = X , B = 2\theta - X $
$ E(Max(A,...
- 387
112
votes
10
answers
27k
views
200
votes
5
answers
57k
views
Why do we need sigma-algebras to define probability spaces?
We have a random experiment with different outcomes forming the sample space $\Omega,$ on which we look with interest at certain patterns, called events $\mathscr{F}.$ Sigma-algebras (or sigma-fields) ...
- 26.9k
71
votes
10
answers
76k
views
Why is the sum of two random variables a convolution?
For long time I did not understand why the "sum" of two random variables is their convolution, whereas a mixture density function sum of $f(x)$ and $g(x)$ is $p\,f(x)+(1-p)g(x)$; the arithmetic sum ...
- 13.3k
31
votes
5
answers
34k
views
Empirical CDF vs CDF
I'm learning about the Empirical Cumulative Distribution Function. But I still don't understand
Why is it called 'Empirical'?
Is there any difference between Empirical CDF and CDF?
- 335
31
votes
6
answers
10k
views
In layman's terms, what is the difference between a model and a distribution?
The answers (definitions) defined on Wikipedia are arguably a bit cryptic to those unfamiliar with higher mathematics/statistics.
In mathematical terms, a statistical model is usually thought of as ...
- 641
11
votes
7
answers
8k
views
Why is the denominator in a conditional probability the probability of the conditioning event?
Quite a simple or at least short question: Why is $ \frac{P(A \cap B)}{P(B)} $ divided by $ P(B) $ for the conditional probability?
$ P(A | B) = \frac{P(A \cap B)}{P(B)} $
Random image to visualize:
...
- 3,493
13
votes
3
answers
2k
views
Why is $x + x = 2x$, but $X + X \neq 2X$?
At this AP central page Random Variables vs. Algebraic Variables, the author, Peter Flanagan-Hyde draws a distinction between algebraic and random variables.
In part he says
$x + x = 2x$, but $X ...
- 2,125
22
votes
4
answers
24k
views
Are "random sample" and "iid random variable" synonyms?
I have been facing hard time understanding meaning of "random sample" as well as "iid random variable". I tried to find out the meaning from several sources, but just got more and more confused. I am ...
- 489
11
votes
4
answers
2k
views
How to interpret sum of two random variables that cross domains?
suppose we have two discrete random variables:
$X: \{$6 sided dice rolls$\}$ $\rightarrow \{1..6\}$ (following uniform distribution)
$Y: \{$coin flips$\}$ $\rightarrow \{0,1\}$ (following uniform ...
- 231
9
votes
1
answer
3k
views
Why do you have to provide a variogram model when you are kriging?
I am very new to spatial statistics and watching lots of tutorials,
But I don't really get why you have to provide a variogram model when you krige.
I am using the gstat package in R, and this is ...
- 3,489
6
votes
3
answers
1k
views
why can two random variables be added only when they have the same domain?
I am watching lecture 7 in harvard stats 110 and the professor is teaching distribution of addition of two random variables and in a breadth says that random variables can be added only if their ...
- 2,693
5
votes
3
answers
3k
views
what exactly does it mean when we say "Let $X_1, X_2 ...$ be iid random variables"
Every now and then I read that phrase and get confused. When we say
"Let $X_1, X_2, \dots X_n$ be iid random variables"
I thought this meant that we are sampling $X$ random variable n many times ...
- 917