Suppose a class is divided into two equal size groups Each s

Suppose a class is divided into two equal size groups. Each student is asked to complete questionnaire. There are 3 questions for Group 1 studnets and 2 questions for Group 2 students. Chance of correct answer is 0.6 for group 1 students and 0.7 for Group 2 students. Let X be the number of questions answerd incorrectly by a randomly chosen student.

(a) Find the probabilty function , p_x(x) = P(X=x) , of the number of incorrectly answred questions.

(b) Find the expected number of incorrectly answered questions.

Solution

a)

0 0.6

1 0.4

2 0.4*0.4=0.16

3 0.4*0.4*0.4 =0.064

b)

expected value

0.6 * 0 + 1 * 0.4 + 2 * 0.16 + 3 * 0.064

0.912