0
votes
2answers
74 views

What is the pdf of $X,Y$?

We know that the common pdf of $X,Y$ is constant function, on the triangle $(0,0),(0,1),(2,0)$ (and out of this range the value of the function is zero). What is $f_X(x)$ and $f_Y(y)$? My solution: ...
1
vote
0answers
39 views

Second moment of random variable in the integral form

Let $X_1,\dots,X_n$ are i.i.d. samples from uniform distribution on $(0,1)$. Let $\hat F_n$ be their modified empirical distribution function defined by $$ \hat ...
0
votes
1answer
22 views

Computing an expectation with a uniform probability distribution.

Suppose $F$ is a cumulative density function of a uniform distribution between $a=0$ and $b=B$ and $c$ is a positive real number. I need to evaluate the integral $$\int_c^Bq\;\mathrm dF$$ where the ...
0
votes
2answers
97 views

Showing the self energies of $N$ uniformly charged disks is proportional to $N^{3/2}$

How would I go about doing this? I assume it is some integral I have to solve, but I have no idea what. (Note:Not a physicist so please excuse incompetence with regard standard notation.) Context ...
4
votes
3answers
880 views

Binomial distribution with Uniform parameter

I have a problem with following exercise (it comes from Geoffrey G. Grimmett, David R. Stirzaker, Probability and Random Processes, Oxford University Press 2001, page 155, ex. 6): Let $X$ have the ...
1
vote
0answers
91 views

Finding Limits of Integration

I have two functions, one depending on $x$ which is $\frac {1} {2} {\delta(x-5)} + \frac {1} {4}$ which is the combination of a dirac delta function at $5$ and a uniform distribution from $5$ to $7$. ...
3
votes
1answer
289 views

Average sine of an angle between two rays in a cone

I'm looking for an average value of sine of an angle between two rays, lying within a cone with a certain angle. Given a cone with an aperture of ${2\chi}$ and two rays lying within the cone. The ...