# 1. Discrete Random Variables. Suppose that we are interested in the number of cups of coffee drank by a (randomly selected) student at UCLA. This quantity can be represented as a random variable Y w

1.Discrete Random Variables.Suppose that we are interested in the number of cups of coffee drank by a (randomly selected) student at UCLA. This quantity can be represented as a random variableYwith probability mass function:ifa_ {0,1,2}ifa= 3ifa= 4,ifa= 5___0 otherwisewherecis an unknown constant.(a)Explain why the number of cups of coffee drank in a day by a randomly selected student at UCLA is a random variable.(b)What is the relevant outcome space of the random variableY?(c)Explain what the distribution of this random variable represents. In other words distribution ofYassigns a probability to any subset of the outcome space. How do we interpret this probability? (d) Solve forc. (Hint:Recall thatPY(OY) = 1 so thatPa_OYpY(a) must equal one).(e)What is the probability that a randomly selected student at UCLA drinks at least 3 cups of coffee a day,PY(Y_ 3)?(f)What is the expected number of cups of coffee drank per day for a randomly selected student at UCLA?