Question

Suppose that 20, 000 married adults in the United States were surveyed as to the number of children they have. The results are compiled and used as theoretical probabilities. Let X equal the number of children, with PDF as per the table below. All entries are to be decimal values accurate to the nearest 0.01 P(x) x. P(x) Collapse Al 0.15 2 0.15 3 0.3 0.2 5 0.05 0.1 a. Complete the table above. b. Determine the expected value. EX] M cIs it more likely that a married adult will have2 to 3 chiloren or 4 to 6 children? pick one Why? pick ane

Answer 1

As per HomeworkLib policy i will answer the first question and its parts. Please post the remaining asking for the rest again

a.

x	P(x)	x*P(x)
0	0.05 (1-sum of the rest=1-0.95)	0
1	0.15	0.15
2	0.15	0.30
3	0.30	0.90
4	0.20	0.80
5	0.05	0.25
6	0.10	0.60

b. The expected value=summation of x*P(x)= 0+0.15+0.30+0.90+0.80+0.25+0.60=3

Therefore the expected value of children=E(X)=3

c. Probability that a married adult will have 2 or 3 children=0.15+0.30=0.45

Probability that a married adult will have 4-6 children=0.20+0.05+0.10=0.35

Therefore it is more likely that a married adult will have 2 or 3 children compared to 4-6 since the sum of the probability is higher in that case.

Hope it helps. Do ask for any clarifications required.