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revprev | Admin | Jun 25'24 at 2:55 | +9 | m | |
revcur | Admin | (Created page with "'''Solution: E''' We have <math display = "block"> E((X-Y)^2]=E[X^2] + E[Y^2] - 2E[XY]=E((X+Y)^2] = E[X^2] + E[Y^2] + 2E[XY]. </math> Hence <math>E[XY] = 0 </math>. Then we also have <math display = "block"> E[X^2] = E[(X-Y)^2] = E[X^2] + E[Y^2]. </math> Hence <math>E[X^2] = 0 </math> which means that <math>P(X=0) = 1 </math>.") | Jun 25'24 at 2:48 | +336 |