Question

answer the following question thank you.

(1) Conditional Mean
Table 1 is the probability of admission to the university. X=1 means that students are admitted; x=0 means that students are not admitted. Students are divided into two groups: male and Female.

Table 1: Admission Table

Admit(x=1) Not Admit(x=0)

Male 0.3 0.2 Female 0.4 0.1

(a) Calculate the probability of admit, the probability of not admit, and the expectation of x.

(b) Calculate the probability of male, the probability of female, the conditional probability of admitting given male, the conditional probability of not admit

given male, the conditional probability of admitting given female, and the conditional probability of not admit given female.

(c)Calculate the conditional expectation of x given male and the conditional expectation of x given female.

(d) Show that the expectation of x equals the expectation of conditional expectation of x.

Answer 1