A multiple choice exam turn five questions and each quotkm h

A multiple choice exam turn five questions. and each quotkm has three choice. of which exactly one is the correct answer. A student completes the exam by guessing. If x is a tain lout variable corresponding to the number of questions the student gets right. then Find the proltabilitv distribution of x. Find E[X] and Var(x).

Solution

The no of choices are 3

correct answer is 1

Hence p = Prob for any question right by guessing = 1/3

Each question is independent of the other and there are two outcomes correct or wrong

Hence

a) X is binomial with no of trials = 5 and p = 1/3

b)E(X) = np = 5/3

c) Var(x) = npq = 5/3(1-1/3)

= 10/9