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Math Help - Convergence in probability and distribution

  1. #1
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    Convergence in probability and distribution

    Let X be the random variable which takes the values 0 and 1 only and is such


    that P[X
    = 0] = P[X = 1] = 1/2. Define the sequence of random variables X, = X for all n and let Y = 1 - X. Now, answer the following,
    justifying your answer in each case:
    (i) Does Xn, converges to X in probability?
    (ii) Does Xn, converges to X in distribution?
    (iii) Does Xn, converges to Y in probability?
    (iv) Does Xn, converges to Y in distribution?

    Ok so i know what the definitions are for both probabiltiy and distribution...i just don't know how to apply them to these types of questions??
    Any kind of help would be helpful....


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  2. #2
    MHF Contributor matheagle's Avatar
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    Are you creating a sequence of IID rvs X_n or is X_n=X ?

    Also Y has the same distribution as X, BUT when X=0, Y=1 and visa versa.
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  3. #3
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    It's equal to X.... Any ideas of how you would go about answering this type of question would be incredibly helpful!!
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