Question

Consider the random experiment of tossing a fair coin three times. Let X be the random variable representing the number of heads that will come out.

a. Construct the probability distribution associated to the given situation.

b. Represent the probability distribution in a) graphically.

c. Compute for the E[X] and Var[[X].

Answer 1

The random variable X represents the number of heads in three coin tosses, and its probability distribution is given by P(X=0) = 1/8, P(X=1) = 3/8, P(X=2) = 3/8, P(X=3) = 1/8.

Step-by-step explanation:

a. The random variable X represents the number of heads that will come out when tossing a fair coin three times.

b. X can take on the values 0, 1, 2, or 3, since there can be 0, 1, 2, or 3 heads when tossing a coin three times.

c. The probability distribution of X is as follows: P(X=0) = 1/8, P(X=1) = 3/8, P(X=2) = 3/8, P(X=3) = 1/8.