**Question:** Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X?

**Solution:**

This is a modified binomial distribution. We are looking at the differences here instead of just the counts. This means that the random variable X ranges from -n to n in steps of 2. Here is one way to design the algorithm

- Perform a series of ‘n’ bernoulli operations (the outcome of each of the operation is either 0 or 1)
- 0 0 0 0 1 0 0 0 1 0

- Then, count the number of fails and passes
- 8 & 2

- Find the difference between the passes and fails
- -6

- Repeat steps one through three and observe the distribution

**Simulation:**

We have seen the algorithm in the solution section and the same will be applied in the code. The charts and the code are given below. Here I have chosen the value of the n = 100. Observer how the values -100 to 100 in increasing steps of 2 are only possible.

End of the Post 🙂

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