What is meant by Expectation or Expected value of a Random Variable? Probability: In terms of Relative frequency. 
$S$: Sample Space of an experiment
$E$: Experiment performed.
For each event $E$ of sample space $S$, we define $n(E)$ : no. of times in first $n$ repetitions of the experiment that the event $E$ occurs. 
$P(E) = \lim_{n \to \infty} \frac{n(E)}{n}$
It is the proportion of time that Event $E$ occurs. 
Is it correct to say that perform the experiment first and then calculate the probable chances of event $E$ to occur depending on the output of our experiment?
Expectation:(What i read from text book) If $X$ is a random variable having a probability mass function $p(x)$ , then expected value of $X$ is:
$E[X] = \sum_{x:p(x)>0}^{}xp(x)$.
What the expectation value of X is describing for X just like probability is describing the proportion of time event $E$ occurs.
$e.g$  $E[X :$ outcome when roll a fair die$]$ = 7/2.
What the 7/2 or 3.5 value signifies? 
I am confused between these two. I understand the probability concept but not expectation. It is better if explains using some example?  
 A: The two concepts are very different. The first one, $\lim_{n\to\infty} \frac{n(E)}{n}$ is a random variable, so it is a map from the probability space to the reals. The second one, the expectation $\mathbb{E}[X]$, is a real number, not a map.
To see the connection, we need to define the random variable $X=1_{E}$, which is the indicator function of the event $E$. In this case, the expectation $\mathbb{E}[X]=\mathbb{P}(E)$ is the probability of the set $E$. On the other hand, the strong law of large numbers tells us that the limit of the random variables $\frac{n(E)}{n}$ as $n\to\infty$ is a (almost surely) constant random variable taking the value $\mathbb{P}(E)$ with probability one.
So, the limit of the relative occurrences is a map which almost surely takes the value $\mathbb{P}(E)$, the expectation of $1_E$ is exactly that value.
The limit of the relative occurrences models an infinitely repeated experiment which approximates the probability of $E$. It is a map, because depending on how the experiment goes, we get a result. The expectation of $1_{E}$ is just the probability of $E$. In the von Mises interpretation of what a probability is, they exactly use this relation provided by the strong law of large numbers. The interpretation says that we should think of the probability of an event as the result of such an infinitely often, independently repeated experiment as described by $\lim_{n\to\infty} \frac{n(E)}{n}$.
