Today we look at some more usages of random variables.  We mentioned so far that random variables can be combined. We know that random variables can be independent and for the different values that it can take, the average value gives a good indication of the summary. Let us take an interesting application of this technique in a hiring problem.  Let us say you wanted to hire an office assistant. We can use indicator random variables with this. Let us first describe the problem. When you hire an office assistant, you may have to interview some candidates. You want to hire a suitable candidate but to actually hire somebody you have more costs. You have to fire the current candidate and you must pay a large hiring fee to the employment agency that is sending the candidates. You are interested in estimating this price This is the hiring problem.
This is written as follows:
int Hire-Assistant(int[] candidates)
{
 int best = -1; // least - qualified dummy candidate
 foreach (var candidate in candidates)
 {
    if (interview(candidate)  > best )
    {
         best = candidate;
    }
 }
hire(best);
return best;
}
We now use probability to analyze this problem. In order to do that, we must use the assumptions about the distribution of inputs. Then we analyze our algorithm and compute an expected run-time.
Since we take the distribution over the inputs, we are averaging the running time over all possible inputs.
We use probabilistic analysis when we can make assumptions about the distribution of inputs i.e. we can assume something about the set of all possible inputs and for designing an efficient algorithm and as a means for gaining insight into the hiring problem. For the hiring problem, we can assume that the candidates are coming in random order. This means we can compare any two candidates in any order and decide who's best.In fact, we can use this fact to establish a distinct ranking of the candidates.
An indicator random variable associated with an event A is defined as 1 if the event occurs and 0 otherwise.
Let us determine the expected number of successes for the interviews. Our sample space is S  = {S, F} and we define a random variable which can take one of the two values of Success or Failure with equal probability. We can then define an indicator random variable which we can express as the event Y = Success. The expected number of successes obtained in one interview is simply the expected value of our indicator variable.