1. The variable x is going to be defined as the number of girls in a three child family. Assume that the probability of having a girl on any given birth is .5. Here is the probability distribution for x. X 0 W P(x) (a) Is this a legitimate probability distribution? Explain. (b) Calculate the mean and standard deviation of this discrete random variable. Make sure to show at least your first and last step if you use technology. Interpret both in context. (c) Describe the events x>1 in words. What is P(x>1)? (d) Express the event "at least two female births" in terms of x. What is the probability of this event