3. A new student majoring in Computer Science at UCI stands in the middle of Aldrich park and randomly asks other students what their major is until they find another CS major. The probability of success is 0.25. (a) What distribution does X follow? State the name and parameters. (b) Compute the expected number of attempts needed before finding another Computer Science major. (c) What is the variance and standard deviation of the number of attempts needed before finding another Computer Science major? (d) What is the probability that the 3rd student asked is the first to be another Computer Science major? (e) What is the probability that it will take less than 6 students before finding another CS major? Compute this value using R and state what function you used. (f) If the student only has time to ask 15 people, what is the probability that he/she will fail to find another CS major? 2 Conditional probabilities Remark. In your answers to all three questions of this section, give an explanation as to why you believe your answer is correct. Marks will not be awarded for answers with numbers not accompanied by any explanation or accompanied by meaningless or irrelevant statements. Consider a department of Computer Science with which 500 students are currently registered. 280 of these students are female and 220 are male. The department offers two undergraduate degrees: Computer Science and Computing with Management. Each student at the department is registered with exactly one of these degrees. In particular, 300 students study Computer Science and 200 students study Computing with Management. Exactly half of the students studying Computer Science are female. Given the above data, please answer the following questions. 1. 10 marks. How many female and how many male students study Computing with Management? 2. 10 marks. What is the probability that a student studies Computer Science provided that this student is male? 3. 10 marks. Infer the probability asked in the previous item using the Bayes formula. Hint: For this you need first to compute the probability that a student is male, the probability that a student studies Computer Science, and the probability that the student is male provided that he studies Computer Science.