2. Let X be a random variable. (a) Show that, if E X2 = 1 and E X4 VE X4 Write x2 |X|™|X|2-, choose r
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- 2 Let X Be A Random Variable A Show That If E X2 1 And E X4 Co Then 1 E X Ve X4 Write X2 X X 2 Choose R 1 (33.92 KiB) Viewed 56 times
2. Let X be a random variable. (a) Show that, if E X2 = 1 and E X4 <co, then 1 E|X|> VE X4 Write x2 |X|™|X|2-, choose r conveniently, and exploit the Hölder inequality. (b) Suppose that E X2m < oo, where m E N. State and prove an analogous inequality.