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

In summary, a joint density problem is a statistical problem that involves finding the probability distribution of two or more random variables. It is different from a single variable density problem as it involves multiple variables and requires the combination of probability distributions. Solving joint density problems is important in various fields and techniques such as joint, marginal, and conditional probability distributions are used. These problems can be solved both analytically and numerically.
  • #1
wuid
40
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
 

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  • Binder1.pdf
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  • #2
Why are you trying to calculate the marginal distribution? Wouldn't it be easier just to integrate the full PDF in polar coordinates again?
 

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

1. What is a joint density problem?

A joint density problem is a statistical problem that involves finding the probability distribution of two or more random variables. This allows for the analysis of how these variables are related and the likelihood of certain outcomes occurring together.

2. How is a joint density problem different from a single variable density problem?

A joint density problem involves multiple variables, while a single variable density problem only involves one variable. In a joint density problem, the probability distribution is calculated for each variable and then combined to determine the overall probability of a particular outcome.

3. What is the importance of solving joint density problems?

Solving joint density problems is important in fields such as statistics, economics, and engineering. It allows for the analysis of complex systems and relationships between variables, which can help in making predictions and informed decisions.

4. What are some techniques used to solve joint density problems?

Techniques such as the joint probability distribution, marginal probability distribution, and conditional probability distribution are commonly used to solve joint density problems. Other methods include the use of probability density functions and cumulative distribution functions.

5. Can joint density problems be solved analytically or do they require numerical methods?

Joint density problems can be solved using both analytical and numerical methods. Analytical methods involve using mathematical equations and formulas to determine the probability distribution, while numerical methods involve using computer algorithms and simulations to approximate the solution.

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