Ability and Codicillary Expectations

30 July 12:38   > >

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The basal abstraction abaft ability is that if your accidental variables (or vectors) are absolute then the aggregate of several of these accidental variable/vectors $left\left(Pleft\left(X_ leq x_, ..., X_ leq x_$
ight)
ight) can be assorted together.

Given $T_, T_,$ are absolute $lambda,mbox$ accidental variables, then $Eleft\left[T_ + T_$
ight] = Eleft[2T_
ight] = Eleft[2T_
ight]. But $mboxleft\left(T_ + T_$
ight) < mboxleft(2T_
ight). This is because $mboxleft\left(T_ + T_$
ight) = mboxleft(T_
ight) + mboxleft(T_
ight) = 2mboxleft(T_
ight) by independence, admitting $mboxleft\left(2T_$
ight) = 2^cdotmboxleft(T_
ight).

See the equations area for some added examples.

`Need   Advice   for Codicillary Exepctation and Codicillary Functions`

(x_),

| align=left | $= F_\left(x_\right) cdots F_\left(x_\right),$

|-

| align=right | $f_\left(x_\right),$

| align=left | $= f_\left(x_\right) cdots f_\left(x_\right),$

|-

| align=right | $Eleft\left[X_cdot X_cdots X_$
ight],

| align=left | $= Eleft\left[X_$
ight] cdots Eleft[X_
ight],

|-

| align=right | $Eleft\left[g_left\left(X_$
ight)cdot g_left(X_
ight)cdots g_left(X_
ight)
ight],

| align=left | $= Eleft\left[g_left\left(X_$
ight)
ight] cdots Eleft[g_left(X_
ight)
ight],

|-

| align=right | $M_\left(x\right),$

| align=left | $= M_\left(x\right) cdots M_\left(x\right),$

|-

| align=right | $F_\left(x,y\right),$

| align=left | $= ???,$

|-

| align=right | $f_\left(x,y\right),$

| align=left | $= ???,$

|-

| align=right | $F_\left(x|y\right),$

| align=left | $= ???,$

|-

| align=right | $F_\left(x\right),$

| align=left | $= Pleft\left(X + Y leq x$
ight),

|}

 Tags: align   ight, align, eleft, cdots, left, mboxleft, independence, conditional, random, , align left, align right, ight ight, ight cdots, ight mboxleft, ight cdots eleft,

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