Please try to answer all the questions.

Sixty students are enrolled in STAT 414. When Cao wants to ask a question, she uses a deck of 60 cards, labeled 1 through 60, to select a person randomly; each card uniquely corresponds to one person. The rule is simple. She randomly picks up a card and calls a name corresponding to the selected card. After calling a name, she puts the card back to the deck and shuffles it before calling the next name. One day, there are 35 STAT 414 students in the class. [a] To ask a question, Cao randomly draws a card from the deck and calls a name corresponding to the selected card. Let us define a binary random variable X1 that is 1 if a student called is in the class and 0 otherwise. Specify the name of Xl's distribution and its parameter value{s}. {b} It is known that one student in the class is called per 15 minutes on average. Let X2 denote the number of students in the class called on that day {in a ?5minute class]. Specify the name of X2's distribution, its parameter value{s}, and possible values {support}. {c} It turns out that Can has drawn 5 cards in total during the class. Let us dene a random variable X3 as the number of selected cards that correspond to students in the class. Specify the name of X3's distribution, its parameter value{s}, and possible values {support}. {d} Cao decides to continue calling names until a person called is in the class. A random variable X4 represents the number of cards drawn until a person called is in the class. Specify the name of X4's distribution, its parameter value{s}, and possible values {support}. {e} What is the probability that Cao has drawn at least 2 cards until she calls a person who is attending the class? If] Cao has drawn 5 cards for 3 questions, i.e., the fifth person called was in the class for the third question. What is the probability of observing this event? [g] It is known that one student in the class is called per 15 minutes on average. Let X5 denote the waiting time until the third student is called. Specify the name of XZ's distribution, its parameter value{s}, and possible values {supportll