Prove that if a sequence of bounded random variables Xnn=1^infty, such that for all n, |Xn|

Name: Prove that if a sequence of bounded random variables Xnn=1^infty, such that for all n, |Xn| < mu < infty, converges in probability, to a bounded random variable X, where |X| < mu < infty, then E[|Xn - X|]n=1^infty converges as a sequence of real numbers to 0, i.e., Xnn=1^infty converges in mean to X.
Uploaded: 2022-05-20T20:34:45-08:00
Duration: 3 min 15 s
Channel: Minh Le
Description: Prove that if a sequence of bounded random variables Xnn=1^infty, such that for all n, |Xn| < mu < infty, converges in probability, to a bounded random variable X, where |X| < mu < infty, then E[|Xn - X|]n=1^infty converges as a sequence of real numbers to 0, i.e., Xnn=1^infty converges in mean to X.

Question

Prove that if a sequence of bounded random variables Xnn=1^infty, such that for all n, |Xn| &lt; mu

Minh Le · Accepted Answer

Step 1:** Write down the definition of expectation, which is equal to the integration of the abs

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