Each question in a 15-question multiple-choice test had 5 possible answers. Suppose you guess randomly on each answer.
a)Show the probability distribution for the number of correct answers.(In a formula using x as the variable.)
b)Verify that the formula E(X)=np for the expectation of the number of correct answers.
Steps shown would be helpful.
[quote=icy;513227]Each question in a 15-question multiple-choice test had 5 possible answers. Suppose you guess randomly on each answer.
a)Show the probability distribution for the number of correct answers.(In a formula using x as the variable.p=1/3,n=15,the rest you can do it
b)Verify that the formula E(X)=np for the expectation of the number of correct answers.
m(t)=(q+pexp^t)^n
m'(t)=npexp^t(q+pexp^t)^(n-1)
let t=0
E(X)=np(q+P)^(n-1)
=np(1-p+p)^(n-1) where q=1-p
=np(1)^(n-1)
=np