Suppose that the university administration becomes very...

Suppose that the university administration becomes very concerned about the amount of partying (and thus lack of studying) done by students. They urge faculty to provide strong incentives for students to study hard. Some professors complain quietly that they will now have to grade carefully all the time, but one economist says there is little need for concern: professors can still throw darts sometimes and make students study. What does she mean? Find the lowest probability that the professor grades carefully that will ensure that students study hard all the time (note that an answer that makes students indifferent between studying and partying is not enough; professors must be sure students will study hard all the time). Professors need to grade carefully with probability

Transcript

00:01 Hello everyone, so this is the question that we have.

00:05 Now 13 % of the students will receive an a.

00:14 32 % will receive b.

00:20 35 % will receive c and 20 % will receive d.

00:31 Now we have a four grading system that a is equal to 4.

00:37 B is equal to three, c is equal to two and d is equal to one and f is equal to zero.

00:47 Remainter will receive f so for part a we need to find the probability distribution for f grade which is a random variable part b we need to give the value of grade and the variance of grade part c we need to give that if the professor has 300 students in each class so we need to give the probability distribution of grades and part d is that he has estimated and he believes in a relationship which is majors is equal to 15 plus 10 class underscore eb a bg which is average we need to be expected value so now expected value and variance of meters now let's jump on to the solution of the question if these are the given constraints so we have all the given probability we convert it into decimal so i would say part we probability of grade equal to fourth is going to be probability of a which is 0 .13 then probability of grade when it is equal to 3 is equal to the probability of b which is 0 .22 then probability of grade equal to two which is probability of grade c which is equal to 0 .35 then probability of grade equal to 1 which is probability of d which is equal to 0 .2 and then probability of grade equal to 0 which is probability of f which is equal to 0 .1 so this is going to be the probability of grade f now coming on to part p expected value so it will be given by e or say grade it is going to be 4 it is grade 4 multiplied by the decimal volume 0 .13 similarly 3 multiplied by 0 .22 this 2 multiplied by 0 .35 plus 1 multiplied by 0 .2 plus 0 multiplied by 0 .1 which is equal to 2 .08 so this is the expected grade or the expected value of rate now if we have to give the variance so e of grade square is going to be 4 square multiplied by 0 .13 plus 3 square multiplied by 0 .22 plus 2 squared multiplied by 0 .35 plus 2 squared multiplied by 0 .35 plus 1 square multiplied by 0 .2 plus 0 square multiplied by 0 .1.

04:23 That is going to be equal to 5 .66.

04:28 Now if i have to give the variance, so where of grade is going to be equal to e of grade square minus the e of grade whole square...

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