Expected Value Properties

In the case of a large collection of assembled numbers, as in the case of the census, one may not be interested in the individual numbers but there may be certain descriptive quantities like average or the median.

This is true in the case of the portability distribution of the numerically valued random variable.

The expected value and the variance are both descriptive quantities that apply only to numerically valued random variables.

If X is the probability density function, then the expected value of X is defined as follows - (assuming that the sum is well defined):
 
P is the probability measure that can be conditional or based on the given event B. 

The expected value of random variables indicates the weighted average. Like the average of probability to get a head-on flipping a coin is 0, 1 or 2.

P (0) = ¼, P (1) = ½, and P (2) = ¼

Hedge fund manager UK needs to include many derivatives and structured products in the portfolio for which they need to select and monitor the performance to examine higher-order return investments.

The predictions through such complex economic functions of financial markets have been higher-order return interactions and historical return data is often nonexistent for the investable funds that are new. 

Interpretation – 

First, the expected value measures the center of probability distribution and long term frequency that is governed by the law of large numbers. 

Like if you bet on 3 numbers between 1 to 12 and if you pick all the numbers correctly, you win $100.

So to find out the expected earnings, if the cost to play is $1, you get X= 100-1
P(X=99) = 1/ (12 3) = 1/220
P(X=-1) = 1-1/220 = 219/ 220
So E(X) = 100*1/220 + (-1)*210 / 220 = -119 / 220= -0.54