Question

One hundred Green hope students take a 10-question multiple choice test with four answers to each question, exactly one of which is correct. All of the students are unprepared and must guess at each question (OH NO!!!) (a) Identify the random variable of interest, and justify your answer.

Answer 1

Explanation:

Given that One hundred Green hope students take a 10-question multiple choice test with four answers to each question, exactly one of which is correct.

For one student , the no of answers he write correctly, say X1 is a random variable which takes values as 0 , 1,2..10

Prob for any one question correct = 0.25 and each question is independent of the other

So X1 is Bino (10, 0.25). Similarly X2, X3...X100 are binomial for each of 100 students.

So random variable is Y = X1+X2+...+X100

This can take values as 0 to 1000 a discrete variable being the sum of 100 independent binomial variables.