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Math Help - Random Parameters

  1. #1
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    Random Parameters

    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?
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  2. #2
    MHF Contributor matheagle's Avatar
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    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
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by mkvbd View Post
    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
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  4. #4
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    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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