SOLUTION: A student writes a multiple-choice test consisting of 3 problems. the first one has 3 possible answers (of which one is correct); the second one has 5 possible answers (of which on

Question 1058040: A student writes a multiple-choice test consisting of 3 problems. the first one has 3 possible answers (of which one is correct); the second one has 5 possible answers (of which one is correct); the third has two possible answers (of which one is correct). The student chooses an answer randomly for each of the three problems.
a) find a sample space
b)find the distribution table of the r.v X representing the number of correct answers the student obtain,
c) compute E(X) and V(X)
d) Find e.d.f F(x) and graph it
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

30 possible solutions in the sample space.
Assume that 1 is the correct answer for each question, all other numbers are incorrect answers.
1,1,1
1,1,2
1,2,1
1,2,2
1,3,1
1,3,2
1,4,1
1,4,2
1,5,1
1,5,2
2,1,1
2,1,2
2,2,1
2,2,2
2,3,1
2,3,2
2,4,1
2,4,2
2,5,1
2,5,2
3,1,1
3,1,2
3,2,1
3,2,2
3,3,1
3,3,2
3,4,1
3,4,2
3,5,1
3,5,2
So then looking at the distribution of correct answers,
3,1
2,7
1,14
0,8
c)

d) What are you looking for here?

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