Convergence in probability

#1
Dear readers,

I have a problem saying:

"Let [X1, X2,....] be a sequence of random variables such that Xn is distributed according to a Bernoulli distribution with parameter (1/n), with n an integer number.
Prove that Xn converges in probability to 0, by obtaining P(|Xn| > Epsolon).

Could you tell me if the solution I provided is correct?

Have you more exercises on this kind of convergence?

Thank you in advance for your future answer

Francesco
 

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