A multiple choice test has 100 questions, each with five possible answers of which one is right The grading scheme is as follows 4 points are awarded for each right answer For each other answer (wrong, missing, etc), one point is taken off that is, 1 points are awarded A student hasn't studied at all and therefore guesses each answer uniformly at random, indepen dently of all the other answers Define the following random variables R the number of answers the student gets right W the number of answers the student does not get right S the student's score on the test 1 3 1 Question 1a What is the distribution ofR Either state the possible values and provide a formula for the probabilities, or provide the name and parameters of the appropriate distribution Explain your answer

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Question: A multiple choice test has 100 questions, each with five possible answers of which one is right. The grading scheme is as follows: 4 points

A multiple choice test has 100 questions, each with five possible answers of which one is right. The grading scheme is as follows:

4 points are awarded for each right answer
For each other answer (wrong, missing, etc), one point is taken off; that is, -1 points are awarded.
A student hasn't studied at all and therefore guesses each answer uniformly at random, indepen- dently of all the other answers.
Define the following random variables:
R: the number of answers the student gets right
W: the number of answers the student does not get right S: the student's score on the test

1.3.1 Question 1a

What is the distribution ofR? Either state the possible values and provide a formula for the probabilities, or provide the name and parameters of the appropriate distribution. Explain your answer.

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