1
vote
2answers
122 views

Too stupid to understand random variable questions?

I have two excercises: 1.) Let $X_1,X_2,X_3$ be independent uniformly distributed random variables on $[0,1]$. What is the density function of $X_1+X_2+X_3$? 2.) Let $X_1,...,X_4$ be independet ...
1
vote
1answer
39 views

Definition of a random variable in the context of a hypergeometric distribution

We defined a random variable in a probability space $(\Omega, E, P)$ as a map $X: \Omega \rightarrow \mathbb{R}$. Unfortunately, I somehow have the impression that this term "random variable is used ...
2
votes
0answers
173 views

Difference of two convex functions

This is an exercise from a probability textbook on Ito's formula, basically Ito's formula extends to functions of this type. Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f$ is ...
7
votes
1answer
150 views

Prove the density of this SDE is not smooth in a parameter

Consider the following, 1-dimensional, equation $$X_t^x = x + \int_0^t \mathbb{E} |X_s^x| \, ds + B_t , $$ where $B$ is a Brownian motion. This a McKean-Vlasov equation, sometimes called a nonlinear ...
0
votes
1answer
132 views

Weak convergence discrete space

Let $X_n$, $n = 1, 2, 3, \ldots$, and $X$ are random variables with at most countably many integer values. Prove that that $X_n \to X$ weakly if and only if $\lim_{n \to \infty} P (X_n = j) = P(X = ...
2
votes
0answers
189 views

Explaining Ito formula to an analyst

From the point of view of analysis, what is Ito formula? Is it an integral by substitution, or, a radon-nikodym derivative? Define the probability space $$ \left(C\left(\Bbb ...