A professor classifies his students according to their grade point average (gpa) and their gender. The accompanying table gives the proportion of students falling into the various categories. One student is selected at random. Gender under 5.0 5.0 to 8.0 over 8.0 male 0.05 0.25 0.1 female 0.1 0.3 0.2 obtain the marginal and conditional distribution functions.
Answers
Answer:
Step-by-step explanation:
Since we already know the student is female, the set of possible females is only 0.6 of the total population.
Following conditional probability. For any two events A and B, where P(B) ≠ 0, the conditional probability is -
P( A | B ) = P( A ∩ B ) / P( B ) = P( B | A) * P(A) / P(B)
where the probability of A given B is equal to the probability of A and B divided by probability of B.
Therefore,
P( GPA between 2 - 3 | Female)
= P( GPA between 2-3 and Female) / P(Female)
= 0.30 / (0.10 + 0.30 + 0.20)
= 0.50
To obtain the marginal and conditional distribution we need to calculate Male and Under 2.0 GPA1P(Male) = 40/100=.40
P(Male|GPA under 2.0) = 5/15 = .33
These probabilities are not equal so being male is related to GPA being under 2.0. So, gender is related to GPA and any two events can work for this.