Random Parameters

**mkvbd** · May 28th 2011, 06:41 AM

Hi,

This is my first post ever in any mathematics forum so forgive me if it is... strange or something. Also, I am not a fan of seeking assistance for assignments so I have been deliberately vague about the problem. Anyway, here it goes.

I have an assignment problem that provides the equation for a continuous random variable, Y, defined by two parameters say $(r,\theta)$ where $\theta$ itself is uniformly distributed over the range (a,b). In part (1) I am required to find the probability density function for R. Part (2) requires me to sketch the pdf of Y over a suitable range for a given value of r.

My reading of the question leads me, in part (1), to integrate Y*(1/b-a) for $\theta$ over the range of $\theta$ . Is this correct or am I way off base? The problem is that if i find f(y) this way I end up with a function without $\theta$ and then, if i put in the given value of r in part (2) I end up with a solution single solution to the equation not a graph over over the range. Have I missed the boat here?

**matheagle** · May 28th 2011, 10:11 PM

It first sounded like r was fixed and $\theta$ was random
Then it sounded like r was random?

I was thinking that you had $f_1(y|\theta)$ and $f_2(\theta)$
I still think you want "I am required to find the probability density function for Y."

If so, the marginal density of Y would be the integral of the joint density from a to b with
integrand f1f2

**CaptainBlack** · May 28th 2011, 10:36 PM

Originally Posted by mkvbd

Hi,

This is my first post ever in any mathematics forum so forgive me if it is... strange or something. Also, I am not a fan of seeking assistance for assignments so I have been deliberately vague about the problem. Anyway, here it goes.

I have an assignment problem that provides the equation for a continuous random variable, Y, defined by two parameters say $(r,\theta)$ where $\theta$ itself is uniformly distributed over the range (a,b). In part (1) I am required to find the probability density function for R. Part (2) requires me to sketch the pdf of Y over a suitable range for a given value of r.

My reading of the question leads me, in part (1), to integrate Y*(1/b-a) for $\theta$ over the range of $\theta$ . Is this correct or am I way off base? The problem is that if i find f(y) this way I end up with a function without $\theta$ and then, if i put in the given value of r in part (2) I end up with a solution single solution to the equation not a graph over over the range. Have I missed the boat here?

Looking at this it seems confused. It looks like $r$ and $\theta$ are not parameters by the polar form of $y$ , a point in the plane.

If this is the case you need to say so and that you are trying to compute the marginal density for $R$ (and that $a=0$ and $b=2\pi$ )

CB

**mkvbd** · June 5th 2011, 11:23 PM

I am sorry for all the confusion and for not following up with my question... I had to focus on my assignment urgently. Well its in now.

I discovered (thankfully before I submitted) that I entirely misunderstood the question. What I needed to do was a transformation using the distribution function method. I am happy and confident with the outcome. However, I find it difficult to know when it is a random parameter and when we are transforming to a new function. Is there an easy way to identify this?

Anyway, thanks for the assistance. In the future I will give myself more time for discussing solutions.

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