Label each of the following statements with =<.>, or NONE. Label a statement with = if equality always holds, with or >

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Label Each Of The Following Statements With Or None Label A Statement With If Equality Always Holds With Or 1 (59.99 KiB) Viewed 81 times

Label each of the following statements with =<.>, or NONE. Label a statement with = if equality always holds, with or > if this inequality or strict inequality holds, and with NONE if none of the above holds. Provide justification for your answers in order to get credit. (i) (5 points) fxy (r, y)dxdy vs. P(x < X <e+da, y <Y <y+dy) if fxy(x,y) > fxy(x+dx, y), fxy(I,y+dy) and fxy(x + dx, y + dy). (ii) (5 points) fx (0) vs. fy(0) if X -U[0,1] (uniformly distributed in the interval [0, 1]) and Y = -InX (iii) (5 points) fxyz(x,y|3) vs. fx|z(+\2) fy|z(y) if X and Y are independent. (iv) (5 points) Fmin(x,y) (1) (cdf of the r.v. min(X,Y) evaluated at 1) vs. Fmax(x,y) (1) if X,Y ~ U[0, 1] (both uniformly distributed) and independent. (v) (5 points) P(limn 400 ) vs P(Y <V2), if X;, i = 1, 2,... are i.i.d with E[Xi] = 0 and Var[X] = 10, and Y~ n(0,10). VS