Question: This is the question: Let Z1, . . . , Zn be a sequence of random variables. For every n = 1, 2, . .

This is the question: Let Z1, . . . , Zn be a sequence of random variables. For every n = 1, 2, . . ., P(Zn = n 2 ) = 1, and P(Zn = 0) = 1 ? 1. In other words, Zn is binary. Show that (a) limn?? E(Zn) = ?. (b) Zn p? 0. (c) Z 2 n + 2019 p? 2019. (d) Does it make sense to apply WLLN and CLT on the mean Z n?

4. Let Z 1 . .... . . In be a sequence of random variables . For every n = 1 , 2 , ... . P ( Un - 2 2 ) = 1 / 2 , and P ( Un = 0 ) = 1 - 1 / 2 . In other words , In is binary . Show that ( a ) limn - too E ( ['n ) = 00 . ( b ) Zin - > O . ( C ) 2 2 + 2019 - > 2019 . ( d ) Does it make sense to apply WLIN and CLI on the mean In

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