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?

The aim of this question is to understand the key concept of a random variable using the coin toss experiment which is the most basic binomial (experiment with two possible outcomes) experiment performed in probability theory.

A random variable is nothing but a mathematical formula used to describe the outcome of statistical experiments. For example, X is a random variable defined as the difference of head and tail outcomes out of n experiments in this question.

The concept of random variables is essential for understanding the further key concepts of process probability and its functions.

Expert Answer

Let:

 total number of coin tosses  = n

And:

 number of tails  = t

Then, the no. of heads can be found using following formula:

 number of heads  = h = n  t

Since X is defined as the difference of total number of heads and tails, it can be calculated using following formula:

X =h  t = ( n  t )  t = h  t  t = h  2t 

Thus possible values of X can be written in mathematical form as:

X = { n  2t | t = { 0, 1, 2, ,, n } }

Numerical Result

 Possible values of X = { n  2t | t = { 0, 1, 2, ,, n } }

Example

A coin is tossed 100 times and tail came up in 45 experiments. Find the value of X.

For this case:

n = 100

t = 45

Hence:

h = 100  45 = 55

X can be calculated using following formula:

X =55  45 = 10

Which is the value of X when 45 tails show up in 100 coin tosses