How Do You Determine the Correct Boundaries for a Marginal Density Function?

  • Thread starter Thread starter wuid
  • Start date Start date
  • Tags Tags
    Density Joint
wuid
Messages
38
Reaction score
0
Hi all

i have problem with my h.w , i think the question is related more to math than to probability, but I'm sure someone here will find how to help me

so i attached my solution with the question, i think i have difficulty to find the right boundaries of the marginal density function of X.

please have a look ,

thx in advance
 

Attachments

Physics news on Phys.org
Why are you trying to calculate the marginal distribution? Wouldn't it be easier just to integrate the full PDF in polar coordinates again?
 

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

Finding marginal distribution of 2d of probability density function
Replies
6
Views
2K
Conditional probability with marginal and joint density
Replies
6
Views
2K
Marginal Probability Distribution
Replies
3
Views
3K
What are the Properties of Joint Density Functions?
Replies
13
Views
2K
Marginal density function understanding
Replies
25
Views
3K
A Quick Multiple choice for marginal density function
Replies
2
Views
2K
Finding Probability Density Functions for Independent Random Variables
Replies
2
Views
2K
Calculating the marginal density function
Replies
1
Views
3K
Understanding Joint Density Functions: Solving for Unknown Parameters
Replies
6
Views
2K
Probability density function for a given problem
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top