When determining characteristics of a variable, there are a variety of data points that can be determined. For all of our examples shown today, we will let X be the random variable with the possible values xi, for i=1,2,…..,n with the corresponding probabilities P(X=xi), i=1,2,,…..n.
Mean:
The mean of a random variable is the average of all the possible values of the random variable.
The series 
if exists is called the mean of random variable X and it is denoted by ‘µ’ .
i.e. Mean, µ =
Variance :
The variance of a random variable measures the variability (or spread) of the distribution.
The series 
if exists is called the variance of a random variable X and is denoted by 
.
i.e. Variance,
Standard deviation: The non negative number which is the square root of variance is called standard deviation and is denoted by 
.
i.e standard deviation, 
Example: When 3 coins are tossed, the probability distribution of X where X denotes the number of heads is,
|
X = r |
0 |
1 |
2 |
3 |
|
P(X =r) |
1/8 |
3/8 |
3/8 |
1/8 |
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