Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads).What is the variance for this distribution?
A)1.5
B)1.22
C)0.75
D)0.87

Question

Quizplus · Accepted Answer

The possible outcomes of tossing a fair coin three times are: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT.
Since the coin is fair, each outcome has probability of 1/8. The expected value of X is E(X) = 3/2. 
To calculate the variance, we use the formula Var(X) = E(X^2) - [E(X)]^2.
We can find E(X^2) as follows:
E(X^2) = (0^2 + 1^2 + 2^2 + 3^2)/8 = 14/8 = 1.75
Therefore, Var(X) = 1.75 - (3/2)^2 = 1.75 - 2.25 = 0.75. 
Thus, the answer is C.

Consider the Experiment of Tossing a Fair Coin Three Times