Let X, - Erponential(n), show that X, 0. That is, the sequence X1, X2, X3, converges...

 

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Let X, - Erponential(n), show that X, 0. That is, the sequence X1, X2, X3, converges in probability to the zero random variable X. ... Solution We have lim P(|X,- 0| 2e) = lim P(X, 2e) ( since X, 20) = lim ( since X,~ Exponential(n) ) 0, for all e > 0. Let X, - Erponential(n), show that X, 0. That is, the sequence X1, X2, X3, converges in probability to the zero random variable X. ... Solution We have lim P(|X,- 0| 2e) = lim P(X, 2e) ( since X, 20) = lim ( since X,~ Exponential(n) ) 0, for all e > 0.

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