math, probability

13. Exercise: Convergence in probability:

a) Suppose that Xn is an exponential random variable with parameter lambda = n. Does the sequence {Xn} converge in probability?

b) Suppose that Xn is an exponential random variable with parameter lambda = 1/n. Does the sequence {Xn} converge in probability?


c) Suppose that the random variable in the sequence {Xn} are independent, and that the sequence converges to some number a, in probability.
Let {Yn} be another sequence of random variables that are dependent, but where each Yn has the same distribution (CDF) as Xn. Is it necessarily true that the sequence {Yn} converges to a in probability?

  1. 👍 2
  2. 👎 0
  3. 👁 85
  1. a) yes
    b) no
    c) yes

    1. 👍 2
    2. 👎 0

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