Did I do this joint density problem correctly?

In summary, a joint density problem is a mathematical problem used to find the probability distribution of two or more random variables. To ensure the correctness of your solution, follow the correct steps and check your answer using the original problem. Common mistakes include using the wrong formula, not considering all given conditions, and incorrect calculations. There are specific methods and formulas for solving joint density problems, such as the joint probability density function, marginal probability density function, and conditional probability density function. You can use a calculator to solve these problems, but it is important to use the correct formula and enter the data accurately, and to show your work for accuracy.
  • #1
miceonparade
1
0

Homework Statement



1. Calculate Fxy(.25,.25)
2. Calculate Fx(.25)
3. Calculate Fy(.25)


Homework Equations



f(xy) = 2 (x+y) if 0[tex]\leq[/tex] x [tex]\leq[/tex] 1 and 0 [tex]\leq[/tex] y [tex]\leq[/tex] x



The Attempt at a Solution



1. without showing all of the steps of my integration (because I apparently can't work this editor too well), I get:

(2/3) * x^3 + (1/3) * x^3 0|.25

= .016



2. (2/3) * x^3 + (1/3) * x^3 0|.25

= .016



3. y + y^2 0|.25
= .3125


Did you guys come up with the same numerical answers as I did for this?
 
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  • #2
.016 is approximately 1/64 so your answers are almost correct.

But why not give exact fractional values?
 

1. What is a joint density problem?

A joint density problem is a mathematical problem that involves finding the probability distribution of two or more random variables together. It is used to model and analyze the relationship between multiple variables in statistics and probability theory.

2. How do I know if I did a joint density problem correctly?

If you followed the correct steps and used the appropriate formulas to calculate the joint density, then there is a high chance that you did the problem correctly. You can also double-check your answer by plugging it back into the original problem to see if it satisfies all the given conditions.

3. What are the common mistakes made when solving joint density problems?

Some common mistakes made when solving joint density problems include using the wrong formula, not considering all the given conditions, and incorrect algebraic calculations. It is important to carefully read and understand the problem before attempting to solve it.

4. Is there a specific method to solve joint density problems?

Yes, there are specific methods and formulas used to solve joint density problems, such as the joint probability density function, marginal probability density function, and conditional probability density function. It is important to understand and apply these methods correctly to solve the problem accurately.

5. Can I use a calculator to solve joint density problems?

Yes, you can use a calculator to solve joint density problems. However, it is important to make sure that you are using the correct formula and inputting the data accurately. It is also recommended to show your work and not solely rely on the calculator's answer.

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