A university posts the grade distributions for its courses online. Students in a

Question

A university posts the grade distributions for its courses online. Students in a class in the fall semester received these grades: 17% A, 9% A, 6% B+, 15% B, 13% B, 4% C+, 22% C, 2% C, 1% D+, 4% D, 2% D, and 5% F. Choose a student at random. To "choose at random" means to give every student the same chance to be chosen. The student's grade on a four-point scale (with

A = 4,

A = 3.7,

B+ = 3.3,

B = 3.0,

B = 2.7,

C+ = 2.3,

C = 2.0,

C = 1.7,

D+ = 1.3,

D = 1.0,

D = 0.7,

and

F = 0.0)

is a discrete random variable X with this probability distribution.

Explanation / Answer

Yes X here which will be a discrete random variable because here the random variable X can only take a value from a set of fixed number of values that are:

{ 4, 3.7, 3.3, 3, 2.7, 2.3, 2, 1.7, 1.3, 1, 0.7, 0 }

Each of the above grade score the student can get with a fixed probability as we are given.

Adding all the probabilities we get:

17% A, 9% A, 6% B+, 15% B, 13% B, 4% C+, 22% C, 2% C, 1% D+, 4% D, 2% D, and 5% F

0.17 + 0.09 + 0.06 + 0.15 + 0.13 + 0.04 + 0.22 + 0.02 + 0.01 + 0.04 + 0.02 + 0.05 = 1

Therefore the sum of the probabilities is 1. Therefore there cannot be any value other than those grade scores from 0 to 4 given. Therefore X which is the grade point here has a discrete distribution.

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