All Questions
24
questions
3
votes
1
answer
130
views
Exercise on Girsanov's theorem
currently I am trying to solve the following exercise.
Exercise: Let $b : \mathbb R → \mathbb R$ be Lipschitz, and let $t \mapsto X(t)$ be the unique strong solution of the 1-dimensional SDE given by
$...
0
votes
0
answers
46
views
Give a lower bound using Chebyshev's inequality
So I am having problems with this exercise. Can someone help me?
The waiting time $T$ in hours for the order in the pizzeria DaFranco has the following density function:
$f_T(X):=\left\{\begin{matrix} ...
- 900
0
votes
1
answer
30
views
How to find the right probability measure and how to be able to distinguish $A \cap B$ from $A|B$
Three machines produce the same car parts and have the following production shares and defect rates:
A part from the total production is selected at random. a) Set up a suitable model $(Ω, F, P)$ ...
- 900
1
vote
1
answer
40
views
Some exercises with a random variable $Z(w)=\left\{\begin{matrix} X(w)& \mbox{if}\ Y(w)\geq 0 \\ -X(w)&\mbox{if} \ Y(w)<0 \end{matrix}\right.$
Hey I want to check my solutions for this problem:
Let $X$ and $Y$ be independent standard normally distributed random variables on a probability space $(\Omega, \mathcal F, \mathbb P)$ and define
$Z(...
- 900
0
votes
1
answer
47
views
Expected value, variance and covariance with discrete random variables
I wamted to check my solutions for this problem:
The joint distribution of the random variables $X$ and $Y$ is given by:
Calculate $E[X], E[Y], Var(X),Var(Y),Cov(X,Y)$
So for $E[X]=1/8+1/4+2(1/8+1/2)=...
- 900
0
votes
2
answers
50
views
Solution verification with conditional probability problem
I want to check my solutions for this problem:
After a weekend seminar, some participants go to a restaurant together on the last evening. $53\%$ of the male seminar participants take part, for the ...
- 900
0
votes
1
answer
44
views
Solutions verification on a problem about probability
I want to check my solutions for this problem.
Klaus and Anna throw tetrahedrons (bodies with 4 triangles as faces) at the same time. Klaus throws 2 tetrahedrons and Anna throws one. What is the ...
- 900
1
vote
1
answer
50
views
Questions on the construction of a stochastic model
I want to check my solutioons for this problem:
The captain of a soccer team is in good form $70%$ of the games, in fair form $20%$ and in poor form $10%$. In these cases, the team's chances of ...
- 900
1
vote
1
answer
194
views
Problems in finding the marginal distribution
I have some problems with this exercise:
Let $X$ and $Y$ be real-valued random variables with a common density:
$f_{X,Y}=\left\{\begin{matrix} 2e^{-x-y} & 0<y<x \\ 0 & else \end{matrix}\...
- 900
0
votes
0
answers
34
views
Calculating distribution and expected values of minimum and maximum of independent uniform random variables
I am having some problems with this exercise, can someone help me?
Let $X_1,X_2$ be independent and identically uniform on $[0,a]$.
Let $U:= \min(X_1,X_2)$ and $V:= \max(X_1,X_2)$.
Calculate the ...
- 900
1
vote
1
answer
49
views
Convergence Properties of Sums of iid Random Variables" [duplicate]
I want to check my solutions for this problem. Can someone help me?
Let $(X_n)_{n\geq1}$ be independent and identically distributed real-valued random variables.
Suppose $E[|X_n|] = ∞$.
a. Show that $...
- 900
1
vote
1
answer
66
views
Show that $P(|X_n| > an \text{ for infinitely many } n) = 1$ for any $a > 0$ with $E[|X_n|] = ∞$
I want to check my solutions for this problem. Can someone help me?
Let $(X_n)_{n\geq1}$ be independent and identically distributed real-valued random variables.
Suppose $E[|X_n|] = ∞$.
a. Show that $...
- 900
1
vote
0
answers
33
views
Probability Measure and Algebraic Structure in Infinitely Repeated Coin Tosses
Hey I want to check my solutions for this problem:
Consider the sample space $\Omega = \{0, 1\}^N$ of an infinitely repeated coin toss. Let $Π_n: \Omega \rightarrow \{0, 1\}^n$ be the coordinate ...
- 900
2
votes
1
answer
468
views
Law of Large Numbers for a Brownian Motion
I am self-learning introductory stochastic calculus from A first course in Stochastic Calculus by L.P.Arguin.
The part(c) of the below exercise problem on the time-inversion property of Brownian ...
- 5,450
4
votes
0
answers
57
views
How can I show that $\bigcap_{n\geq 0} \sigma(X_n,X_{n+1}...)=\sigma(X)$?
Let $X$ be a uniformly distributed random variable in $[0,1]$ and define $X_n:=\lfloor 2^nX\rfloor 2^{-n}$ for all $n$. I want to show that $\bigcap_{n\geq 0} \sigma(X_n,X_{n+1}...)=\sigma(X)$.
My ...
- 2,018