A senior student, Zico, starts to manage his own banking account. His initial deposit is $2,000. Meanwhile, he starts to tutor 10 high school students in Calculus. Every week, each student contacts Zico for tutoring with a probability of p = 0.8. If a student contacts Zico, Zico earns $50 and deposits it into his banking account; otherwise, he needs to withdraw $20 for his living expense. Suppose that each student contacts Zico independently every week. 

a) Find the probability distribution of the number of tutor sessions each student needs after 5 weeks. (4 marks)
b) Find the expected number of session each student needs after 5 weeks and the corresponding variance by definition. (3 marks) 

c) Find the expected amount of deposit in Zico's banking account after 5 weeks and the corresponding variance by definition. 

Answer rating: 100% (QA)

To solve this problem we will use the concepts of probability distribution and expected value a Find the probability distribution of the number of tut... View the full answer