Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

Question

Philoid · Accepted Answer

Given: A coin is tossed 6 times.

X represents the difference between the number of heads and the number of tails.

⇒ X(6H, 0T) = |6-0| = 6

X(5H, 1T) = |5-1| = 4

X(4H, 2T) = |4-2| = 2

X(3H, 3T) = |3-3| = 0

X(2H, 4T) = |2-4| = 2

X(1H, 5T) = |1-5| = 4

X(0H, 6T) = |0-6| = 6

Therefore, X is a function on sample space whose range is {0, 2, 4, 6}.

Thus, X is a random variable which can take the values 0, 2, 4 or 6.