Question

The probabilities below reveal the intergenerational income movement. Mother= Bottom Third, Daughter = Bottom Third, Probability = 0.6; Mother= Bottom Third, Daughter = Middle Third, Probability = 0.25; Mother= Bottom Third, Daughter = Top Third, Probability = 0.15; Mother= Middle Third, Daughter = Bottom Third, Probability = 0.25; Mother= Middle Third, Daughter = Middle Third, Probability = 0.5; Mother= Middle Third, Daughter = Top Third, Probability = 0.25;Mother= Top Third, Daughter = Bottom Third, Probability = 0.15; Mother= Top Third, Daughter = Middle Third, Probability = 0.25; Mother= Top Third, Daughter = Top Third, Probability = 0.6. Find the probability that the granddaughter (along the maternal line) of a woman in a top third of the income distribution will remain in this group.

a. .80

b. .60

c. .45

d. .25

Answer 1

to find :

probability of granddaughter in the top third of the income distribution given that the woman is also is in top third income distribution.

the woman's daughter can be in any of the 3 income distributions.

we will need the following probabilities :

Mother= Top Third, Daughter = Bottom Third, Probability = 0.15;

Mother= Bottom Third, Daughter = Top Third, Probability = 0.15;

Mother= Top Third, Daughter = Middle Third, Probability = 0.25;

Mother= Middle Third, Daughter = Top Third, Probability = 0.25;

Mother= Top Third, Daughter = Top Third, Probability = 0.6;

and we can have the following possibilities :

woman	daughter	granddaughter	probabilities	total probabilities
top third	top third	top third	0.6*0.6	0.36
top third	middle third	top third	0.25*0.25	0.0625
top third	bottom third	top third	0.15*0.15	0.0225
			total	0.445

note : the woman's daughter is the mother of the granddaughter.