Ability and Codicillary Expectations

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 30 July 12:38   > >

    ----

    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(Pleft(X_ leq x_, ..., X_ leq x_
ight)
ight) can be assorted together.

    Given T_, T_, are absolute lambda,mbox accidental variables, then Eleft[T_ + T_
ight] = Eleft[2T_
ight] = Eleft[2T_
ight]. But mboxleft(T_ + T_
ight) < mboxleft(2T_
ight). This is because mboxleft(T_ + T_
ight) = mboxleft(T_
ight) + mboxleft(T_
ight) = 2mboxleft(T_
ight) by independence, admitting mboxleft(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_(x_) cdots F_(x_),

    |-

    | align=right | f_(x_),

    | align=left | = f_(x_) cdots f_(x_),

    |-

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

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

    |-

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

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

    |-

    | align=right | M_(x),

    | align=left | = M_(x) cdots M_(x),

    |-

    | align=right | F_(x,y),

    | align=left | = ???,

    |-

    | align=right | f_(x,y),

    | align=left | = ???,

    |-

    | align=right | F_(x|y),

    | align=left | = ???,

    |-

    | align=right | F_(x),

    | align=left | = Pleft(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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