Question

If a fair coin is tossed n times and x denotes the average number of heads, then distribution of x satisfies

Answer 1

In any coin toss the P(H) = P(T) = 12

A fair coin is tossed thrice. The sample space of three tosses of a coin is: {HHHTTTHHTTTHHTHTHTHTTTHH}

If X is the random variable, we can see that X = 0, 1, 2 or 3 depending on the # of heads.

P (X = 0) = P (no heads) = P (TTT) = 18

P (X = 1) = P (HTT, TTH and THT) = 38

P (X = 2) = P (HHT, HTH and THH) = 38

P (X = 3) = P (HHH) = 18

Therefore, given this probability distribution we can calculate the mean using the formula Mean of the probability distribution = ∑(Xi×P(Xi))

⇒ Mean =0×18 +1×38 +2×38 +3×18=128=32