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Characteristics of random variables

 

Mathematical expectation. Properties of mathematical expectation.

Variance. Properties of variance. Root-mean-square deviation.

 

Mathematical expectation of a discrete random variable  X , which receives a finite number of values  i  with probabilities  i , is called the sum:

 

( ) = 1 1 + 2 2 + 3 3 + ... + n n .

 

Properties of mathematical expectation:

 

   1)   (   ) =   ( ) ,   c R ,

 

   2)   ( + Y ) = ( ) + ( Y ) ,     , Y ,

 

    3)   (   Y ) = ( ) ( Y )   for independent random variables    and  Y

 

Variance of a random variable  X  is called the number:

 

 D ( ) = { [ ( )] 2 }= ( 2 ) [ ( )] 2 .

 

Properties of variance:

 

   1)   D (   ) = 2  D ( ) ,   c R

 

   2)   D ( + Y ) = D ( ) + D ( Y )   for independent random variables    and  Y

 

Root-mean-square deviation:

 

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