A multiplechoice test contains 5 questions each with four an

A multiple-choice test contains 5 questions, each with four answers. Assume a student just guesses on each question.

1) What is the range of the random variable X, the number of questions the student answers correctly?

2) Construct the probability mass function for the random variable X, the number of questions that the student answers correctly.

Solution

1.

X = {0,1,2,3,4,5}

As he can only have 0 to 5 correct answers, as there are just 5 items.

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2.

Using binomial distribution formula,

P(x) = nCx p^x (1-p)^(n - X)

As

n = 5
p = 1/4 = 0.25,

P(X) = 5CX (0.25^X) (0.75^(5-X)) [ANSWER]

where 5CX = 5!/(X!(5-X)!).