I have 20 students, 1000 questions with five options a, b, c, d, e. First, I am using rmultinom(1000,1,c(0.2,0.2,0.2,0.2,0.2) to generate the truth. Next, I want to simulate what a student chooses for each question.
Suppose for Q1, the correct answer is a, I need to simulate the probability of student 1 of choosing the correct answer to be higher than the truth. And then let the choice be uniform for the other 4 choices.
Which probability function should I use to simulate the answers?