Cauchy Random Variable Homework with Equations and Attempt

ahamdiheme
Messages
24
Reaction score
0

Homework Statement


I have attached the problem statement


Homework Equations



Also find attached

The Attempt at a Solution



My attempt is attached together with the problem statement and the relevant equations.
 

Attachments

Physics news on Phys.org
Is anyone going to help me out on this one? I need your help. Here i will re-post as .jpg. Thank you
 

Attachments

  • Problem.jpg
    Problem.jpg
    25 KB · Views: 447

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Break a Stick Example: Random Variables
Replies
1
Views
1K
Getting the probability distribution of a random variable
Replies
2
Views
1K
MSE estimation with random variables
Replies
1
Views
1K
Finding Probability Density Functions for Independent Random Variables
Replies
2
Views
2K
Sum of the Expected Values of Two Discrete Random Variables
Replies
4
Views
3K
Probability: pair of random variables
Replies
5
Views
1K
Calculating the covariance of two discrete random variables
Replies
2
Views
1K
Expected value of a function of a random variable
Replies
5
Views
1K
Sinusoidal sequences with random phases
Replies
1
Views
1K
What is the distribution of the sum of n iid Bernoulli random variables?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top