Please explain how to solve part c, part d, part e, part f with details on how to solve Thank you

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 with probability mass function: g if a e {0, 1, 2} g c=3 py(a) = % if a = 4 , c if a = 5 0 otherwise where c is an unknown constant. (c) Explain what the distribution of this random variable represents. In other words distribution of Y migns a probability to any subset of the outcome space. How do we interpret this probability? ((1) Solve for c. (Hint: Recall that Py(0y) = 1 so that EQEOY py(c) must equal one). (B) What is the probability that a randomly selected student at UCLA drinks at least 3 cups of coffee a day, Pyl' 2 3)? (1') What is the expected number of cups of coffee drank per day for a randomly selected student at UCLA