Linked Questions

2
votes
0answers
215 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 ...
0
votes
0answers
25 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,...
89
votes
9answers
18k views

What is meant by a "random variable"?

What do they mean when they say "random variable"?
181
votes
4answers
42k 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) ...
54
votes
10answers
55k 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 ...
24
votes
5answers
24k 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?
29
votes
6answers
7k 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 ...
13
votes
3answers
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 ...
20
votes
4answers
19k 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 ...
7
votes
4answers
800 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 ...
9
votes
1answer
2k 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 ...
6
votes
3answers
421 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 ...
1
vote
1answer
1k views

How to find the variance in this neural network related question?

I have been going through Neural Networks and Deep Learning. There is a way to represent the activation of network as: z = summation of(w*x) + b where w,b are weight and bias with mean of 0 and S.D ...
4
votes
3answers
718 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 ...
2
votes
1answer
600 views

Expectation of a cubic transformation of a Bernoulli random variable

I was asked the following question: $X$ is a random variable which follows a Bernoulli distribution with parameter $p$ and take $Y=a+bX$. Compute $\mathbb{E}(Y^3)$.

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