{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

peafinal02-sol

# peafinal02-sol - SOLUTION PEA Final Examination Thursday...

This preview shows pages 1–3. Sign up to view the full content.

12/10/03 12:48 PM 1 SOLUTION PEA Final Examination Thursday December 16, 2002 All six questions required for full grade. Please give explicit numerical answers wherever possible, on the same page as the question. Q1 15 Q2 15 Q3 20 Q4 15 Q5 15 Q6 20 TOTAL 100

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
12/10/03 12:48 PM 2 1. A class is taking a multiple-choice test. For any question on the test, the fraction of examinees that knows the answer to every question is p ; 1-p is the fraction that guesses. The probability of answering a question correctly is 1 for an examinee who knows the answer and 1/m for a guesser, where m is the number of multiple-choice alternatives. p=0.8, m=5 a. (7) What is the probability that an examinee answers a question correctly? P[knows] = p; P[guesses]=1-p; P[correct|knows]=1; P[correct|guesses]=1/m. P[correct] = P[correct|knows]P[knows] + P[correct|guesses]P[guesses] = p × 1 + (1-p) × 1/m = 1/m + p × (m-1)/m = 0.84 b. (4) Compute the probability that an examinee knew the answer to a question given that he or she has answered it correctly. P[knows|correct] = P[correct|knows]P[knows] / P[correct] = mp / (1 + (m-1)p) = 0.95 c. (4) Compute the probability that an examinee answers two specific questions correctly. P[correct1,correct2] =P[correct1,correct2|knows]P[knows] +P[correct1,correct2|guesses]P[guesses] =p + (1-p)/m 2.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

peafinal02-sol - SOLUTION PEA Final Examination Thursday...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online