Final answer:
The random variable X represents the number of boys in a family with three children, which can take values 0, 1, 2, or 3. Its distribution is binomial with n=3 and p=0.5. The non-relevant part about having no children does not apply to X as defined.
Step-by-step explanation:
Defining the Random Variable X
In words, the random variable X represents the number of boys in a family with three children. Considering each child can either be a boy or a girl with an equal chance, the random variable X can take on the following values: 0 (no boys), 1 (one boy), 2 (two boys), or 3 (three boys). The distribution of X will follow a binomial distribution with n=3 trials and a probability p=0.5 for each trial (assuming the probability of having a boy or a girl is equal).
The statement "Find the probability that she has no children" does not seem relevant to the scenario of the random variable X defined as the number of boys in a family with three children.