The probability of winning a war not only depends upon the capacity of the country but to a large extent it depends upon the capacities of the opponent.The variance in the success rate also depends upon the other country.

Calculating the variance of a random variable with respect to another variable is called Co-Variance.The concept of co-variance is very useful for problems involving dependent variables

Now let us see how to calculate the co-variance

The sequence of probabilities P(X=x_i),which will be written more conveniently as p(x_i),x=1 ,2 ,3 ,....,is called a probability distrubutionof the random variable X.

The function f_x(x)is called the probability density funtion (pdf) of random variable X.

The joint cdf of the bivariate random variable (X,Y)is given by

A simple and convenient characterization of joint pdf is given by (1,1) central moment that is called covariance of X and Y and is written as Cov(X,Y):

The correlation coefficient of random variables X and Y is given by