Modeling & Simulation

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3. At Al-Azhar University, each student has a probability of 0.6 to pass the simulation exam. Denote by N the random variable that represents the number of times a student must take the simulation exam in order to pass it (assume independent outcomes for each trial, and that probability of success remains the same). (i) (1 mark) What is the distribution for N? (a) exponential (b) geometric (c) binomial (d) uniform (ii) (212 marks) What is the average number of times a student has to take the exam? (a) 0.6 (b) 1 (c) 1.2 (d) 1.67 (iii) (22 marks) In a class of 35 students, what is the average number of people that will pass the exam (at that particular semester's examination)? (a) 18 (b) 20 (c) 21 (d) 24