A bag contains 5 red and 5 blue balls. Select two at random without replacement. If they are of the same color you win $1.10 otherwise you lose $1. Let X be your winnings. Compute EX and Var(X).

And if we find the variance for the indicator variable we got:

Step-by-step explanation:

For this case we can define an indicator variable I that is 1 when we win and 0 when we not win.

And we can define the random variable X as the amount of money that we can win like this:

We can find the probability of win like this:

And the probability of no win would be:

The two possible values for X are 1.1 when we win and -1 when we not win.

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).  

We can find the expected value with this formula:

And if we replace the values that we have we got:

Now in order to find the variance we need to find the second moment defined as:

And if we replace we got:

We can calculate the variance using this definition:

And if we find the variance for the indicator variable we got: