Jointly distributed Rv

  1. Hi ,
    I got this question in my midterm today but up till now I don't know how to solve it ,

    The Question is as follow :
    If X and Y are two exponential Rv with different lambda . and there's a new Rvs Z and U are defined such that :

    Z= 0 : X<Y and 1 : X=> Y

    U= min(X,Y)

    and the Question asked to proof that Z and U are independent .

    So I started my solution by deriving the pdf of U since I know how to then tried to derive the pdf of Z but didn't know where to start and got stuck . :frown:

    Can anyone tell me of a way to derive the pdf of Z . or is there another way to solve the problem ???:uhh:

  2. jcsd
  3. Z is discrete and doesn't have a pdf - one way around is to consider the cdf instead, i.e. show that the joint cdf of Z and U is a product of the marginal cdfs.
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