Marginal pdf, what am I doing wrong?

[Rifscape]

Homework Statement

f(xy)=49/8*e^(−3.5*y) 0 < y < inf and −y < x < y

0 otherwise

a. Find the marginal probability density function of X, fX(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for division, ^ for power, abs for absolute value and exp for exponential function. For example, 3abs(x-5)exp(-x/2) means 3|x-5|e-x/2. Use inf for ∞ and -inf for -∞.

I'm not sure what I am doing wrong here, I keep getting 7/4 and the bounds are from -inf to inf right?

Homework Equations

The marginal pdf equation for x.

The Attempt at a Solution

I did the 8/49*∫e^(-3.5*y) from 0 to inf and got 7/4 with the bounds of x being from 0 to inf. What exactly am I doing wrong?

Or would the bounds be from x to infinity? Any advice is appreciated.

Thanks for the help

 

[LCKurtz]

First of all I think you should check the problem is typed correctly. I don't think what you have given is a density function. Second, draw a picture of the region where $f(x,y)\ne 0$. You need to know that to know the correct limits for your integrals.

 

[Rifscape]

First of all I think you should check the problem is typed correctly. I don't think what you have given is a density function. Second, draw a picture of the region where $f(x,y)\ne 0$. You need to know that to know the correct limits for your integrals.

You're right, it was 49/8 not 8/49 for the constant. I tried drawing the picture, I got that the bounds seem to look like its from -inf to inf. But for the distribution wouldn't I have to get x in terms of y? That's why I thought the bounds would be from -x to x, since x < y and y > -x.

 

[LCKurtz]

You're right, it was 49/8 not 8/49 for the constant. I tried drawing the picture, I got that the bounds seem to look like its from -inf to inf. But for the distribution wouldn't I have to get x in terms of y? That's why I thought the bounds would be from -x to x, since x < y and y > -x.

Your original statement of the problem had limits: 0 < y < inf and −y < x < y. That is the region where your $f(x,y)\ne 0$. Now, the definition of the marginal density is$$
f_X(x) = \int_{-\infty}^\infty f(x,y)~dy$$You only have to integrate over the region where $f(x,y)\ne 0$. For each $x$ you integrate in the $y$ direction. When $x<0$ where does $y$ go? When $x>0$ where does $y$ go? You need to look at your region. So let's see how you set up that integral.

 

[Rifscape]

Your original statement of the problem had limits: 0 < y < inf and −y < x < y. That is the region where your $f(x,y)\ne 0$. Now, the definition of the marginal density is$$
f_X(x) = \int_{-\infty}^\infty f(x,y)~dy$$You only have to integrate over the region where $f(x,y)\ne 0$. For each $x$ you integrate in the $y$ direction. When $x<0$ where does $y$ go? When $x>0$ where does $y$ go? You need to look at your region. So let's see how you set up that integral.

Would I need to split it up and integrate x from -inf to 0, and then integrate x from 0 to inf?

 

[LCKurtz]

When $x<0$ where does $y$ go? When $x>0$ where does $y$ go? You need to look at your region. So let's see how you set up that integral.

Would I need to split it up and integrate x from -inf to 0, and then integrate x from 0 to inf?

You aren't integrating $x$. It it is a $y$ integral. You could start by answering the two questions I asked you above. It would also help if you would describe the region in words so I know you have the correct region in the first place.