A particular professor is known for his arbitrary grading policies. Each paper receives a grade from the set {$A , A- , B , B- , B+, C+$}, with equal probability, independently of other papers. How many papers do you expect to hand in before you receive each possible grade at least once?
question as i understood it
i turn in a paper and i get a grade back and then i turn in another paper and i get a grade and so on. how many paper i have to write before getting all kinds of grades at least once.
my wrong answer
let $B_X$ represent the geometric random variable that represents the number of papers i had to write to get at least one paper graded as $X$
for grade $A \space$, $E[B_A] = 6$ (since there are six grades and all are equally likely, $ P(A)=1/6$)
so on an average, i should have gotten at-least one paper graded as A after writing 6 papers
since $E[B_X] = 6$ ,for all grades $X \space$ in this case.
Hence if talking about an average case scenario,
after 6 papers i should have at-least one paper graded as X (for all X), because that is the definition of expected value.