Questions about maps from a probability space to a measure space which are measurable.
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votes
1answer
19 views
Conditional distribution of a function of random variables
I have a question about conditional distribution. Suppose we have three independent random variables $X_1$, $X_2$, $X_3$.
Then we have mapping $Y_1=g(X_1, X_2)$. The mapping is not necessarily an ...
1
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2answers
18 views
Results about conditional expectations
$\theta$, $\phi$ are integrable random variables on a probability space $(\Omega,\mathcal{F},P)$ and $\mathcal{G}$ is $\sigma$-field on $\Omega$ contained in $\mathcal{F}$.
Now we want to prove ...
0
votes
1answer
22 views
How do you calculate the expected value, the variance and the standard deviation of a sum of random variables, regardless of their distribution
I was looking for a formula or something, but I can't find anything anywhere. So, can someone tell me the steps I need to follow in order to do that? I thought that the expected value of the sum was ...
4
votes
1answer
29 views
Density function of $\max(X_1,\dots,X_n)$.
I'm making this statistics exercise and I'm not sure about my solution.
Find the density function of $Y=\max(X_1,\dots,X_n)$ if they are all i.i.d.
This was my take on this question: $F_Y(a)=P(X_1 ...
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votes
0answers
26 views
Asking for kind help on deriving the probability distribution of p^p?
Hello to Kind Viewers of This Question!
I have a question and don't know where to begin solving it. Please help!
Let X be a binomially distributed random variable with parameter's (n,p).
So p is ...
1
vote
1answer
38 views
Convergence in Probabiliy
$X_n$ converges to $0$ in probability and a sequence of constants $|c_n|$ diverges to infinity. Can someone please help me prove that $X_n - c_n$ does not converge to $0$.
(I am totally blank as to ...
0
votes
0answers
49 views
Piecewise Transformation of Random Variables
Given:
Independent uniform random variables: $X_1\sim\mathrm{Uniform}(-0.10,0.10)$ and $X_2\sim\mathrm{Uniform}(-0.05,0.05)$.
Functions:
$$Z=g\left(X_1,X_2\right)=\mathrm{a}\frac{X_2-1}{X_1-1}$$
...
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votes
1answer
43 views
independent, identically distributed (IID) random variables
I am having trouble understanding IID random variables. I've tried reading http://scipp.ucsc.edu/~haber/ph116C/iid.pdf, http://www.math.ntu.edu.tw/~hchen/teaching/StatInference/notes/lecture32.pdf, ...
-3
votes
1answer
34 views
Expression of Discrete and Continuous random variables.
Let $X$ be a discrete random variable. And let $Y = cX$ for some constant $c$.
How can you express the distribution of $Y$ in terms of the distribution of $X$?
Let $X$ be a continuous random variable ...
0
votes
1answer
41 views
What is a sample space supposed to be?
In this paper, Robert Aumann claim that(page 508):
But as shown at the bottom of page 520, all these sample spaces don't admit uncountable independent random variables.
What's the implication of ...
1
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3answers
33 views
Finding unknown values from discrete probabilities.
(I am confused here with the limits. It says x = 0,1,2,3... So what is my end limit her? Thanks.)
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votes
0answers
48 views
Show that there is no unbiased estimator
I have to solve this problem:
X~$B(n,\theta)$. Show that there is no unbiased estimator of $g(\theta) = \frac{1}{\theta}$ based on X.
1
vote
0answers
41 views
Proving a variable as discrete random (confusing question)
A box contains 3 white and 3 black marbles. In a game, 3 marbles are randomly selected from the box. The score (X) is equivalent to the getting of 10 white marbles. Show that X is a discrete random ...
2
votes
0answers
29 views
Joint distribution between a uniform random variable and a function which is “almost” independent from it
Motivation
Let $f(\cdot)$ be a (possibly randomized) function, such that for any random variable $X$ (taking values from a finite set $D$), $X$ and $f(X)$ are statistically independent. Let $U, U_1, ...
1
vote
2answers
44 views
Forming probability distributions of type $W=X+Y$.
I am able to do part a) easily. My only problem here is finding the prob. distribution for $w=x+y$. If I could get that, I can solve c) also. Also, will it be the same case for $w=x-y$? Theres a ...
