2. 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

Question

2. 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, indepenently of other papers. How many papers do you expect to hand in before you receive each possible grade at least onc?

in progress 0
Remi 2 weeks 2021-11-22T02:04:36+00:00 1 Answer 0

Answers ( )

    0
    2021-11-22T02:06:28+00:00

    Answer:

    14.7

    Step-by-step explanation:

    Total number of grades= 6

    Imagine Y to be number of papers till we get all grades once. Hence

    Yi= Number of papers till we get i th newer grades

    Expected value of Y₆= ?

    The difference between getting a new grade maybe represented as

    Xi= Yi+1 – Yi

    Using above equation for Y₆, we get

    [Y₆]= ∑⁵i=o Xi

    which means, we need to get 5 different grades from the first grade.

    Number of tries to see second new grade maybe represented as

    X₁= {(6-1)/6}, which, for generalization is written as Xi=geo{(6-i)/6}

    Xi represents the success probability of seeing further new grade.

    Expected value of Xi is inverse of parameter of geometric distribution, which is

    [Xi] = 6/(6-i) = 6.{1/(6-i)}

    Expected value of Y₆= [∑⁵ i=0 Xi] = ∑⁵ i=0 [Xi]

    Substituting value of [Xi] in the above expression

    6.∑⁵i=0 {1/(6-i)} = 6. ∑⁶i=1 (1/i)

    Now solving for 6 grades

    Y₆ = 6[(1/6) + (2/6) + (3/6) + (4/6) + (5/6) + (6/6)]

    Y₆ = 6 x 2.45 = 14.7

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )