ALL ABOUT STATISTICAL THEORY

1. A student answers a multiple choice examination question that has 4 possible answers. Suppose 4. 5. that the probability that the student lmows the answer to the question is ELSE) and the probability that the student guesses is 0.21]. If student guesses, the probability of correct answer is [1.25. (a) [4 points) What is the probability that the question is answered correctly? {b} [3 points]I If the question is answered correctly, what is the probability that the student in fact knew the correct answer and was not guessing. [5 points) Let A and B be two events that are independent. Prove that their complements are also independent. Consider the experiment of rolling a loaded die in which the chance of observing an odd number of dots is twice as likely as observing an even numbers of dots. Dene X as the number of dots observed when rolling the die. (a) [4 Points} Give the probability mass function of X. {b} [4 points]I Give the cumulative distribution function of X and sketch its graph. (6 points] In a family of 7 children, what is the probability that there will be more boys than girls? Pat is required to sell candy bars to raise money for the IE"? grade eld trip. There is a 4% chance of him selling a candy bar at each house. He has to sell 5 candy bars in all. (a) (3 points} What is the probability he sells his last candy bar at the 11all house? (b) [5 points} What is the probability of Pat nishing on or before the 8th house? [e] [2 points} What is the expected number of houses needed to sell all 5 candy bars? (d) [2 points) What is the variance of the number of houses needed to sell all 5 candy bars