Each of 40 multiple choice questions on an exam has five possible answers, where

Question

Each of 40 multiple choice questions on an exam has five possible answers, where only one is correct. A particular student chooses the strategy of selecting an answer randomly. Continue with problem 1. (a) Specify the distribution of n_i, where n_i = the number of times the student picked answer i, i = 1, 2, 3, 4, 5. (b) Find the expected value and variance of n_i. (c) What is the probability that the student picks each choice exactly 8 times (8 (a)'s, 8 (b)'s, 8 (c)'s etc..). (d) What is the correlation between n_1 and n_2?

Explanation / Answer

Solution : ( 1 )

( b )

n = 40, p = 1/5, q = 4/5

mean = n * p = 40 * 1/5 = 8

and

variance ² = n * p * q = 40 * (1/5) * (4/5) = 32/5 = 6.4

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