Question
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?
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?
Answers
a) yes
b) no
c) yes
b) no
c) yes
y
n
n
n
n
142n=47 find n