Question

Consider the following joint probability distribution for random variables: hourly wage in dollars, wage, and years of education, educ.

wage = 5 wage = 10 wage = 15

educ = 12 1/6 1/12 1/12

educ = 14 1/12 1/6 1/12

educ = 16 1/12 1/12 1/6

1) What is E(educ)?

2) What is E(wage)?

3) What is P(wage = 5 | educ = 12)?

4) What is P(wage = 10 | educ = 12)?

Answer 1

Data:

		wage, w			Probaility, p	p*e
		5	10	15
educ, e	12	0.1667	0.0833	0.0833	0.3333	4
	14	0.0833	0.1667	0.0833	0.3333	4.666667
	16	0.0833	0.0833	0.1667	0.3333	5.333333
	Probability, p	0.3333	0.3333	0.3333
	p*w	1.66666667	3.333333	5

1.

E(educ) = 4 + 4.667 + 5.33

= 14

2.

E(Wage) = 1.667 + 3.33 + 5

= 10

3.

P(wage = 5 | educ = 12) = 0.1667/0.333

= 0.5

4.

P(wage = 10 | educ = 12) = 0.0833/0.3333

= 0.25

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