(1) Conditional Mean Table 1 is the probability of admission in the university. X=1 means that...

(1) Conditional Mean Table 1 is the probability of admission in 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, conditional probability of admit given male, conditional probability of not admit given male, conditional probability of admit given female, and 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 to the expectation of conditional expectation of x

Expert Solution

orchestra answered 1 year ago

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