Respuesta :
Answer:
0.54,0.46,0.43
Step-by-step explanation:
Given that India is the second most populous country in the world, with a population of over 1 billion people.
The pdf of household size say X in India varies from 1 to 8.
The distribution is shown as follows
X 1 2 3 4 5 6 7 8 Total
P 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 1.00
a) the probability that there are less than 5 members in a household in India
=[tex]P(X<5)[/tex]
=[tex]P(1 to 4) = 0.54[/tex]
b. the probability that there are 5 or more members in a typical household
in India
=[tex]P(X\geq 5) = P(5 to 8)\\\\= =0.46[/tex]
c) the probability that the number of members in a typical household in India is strictly between 2 and 5
[tex]=P(2<x<5) = P(3)+P(4)\\=0.43[/tex]
The probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively
Probability distribution
Given the probability distribution for the household size in India as shown;
X 1 2 3 4 5 6 7 8 Total
P 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 1.00
a) The probability that the number of members in a typical household in India is strictly less than 5 is given as:
P(X < 5) = P(X=1) + P(X=2) + P(X=3) + P(X=4)
P(X < 5) = 0.02+ 0.09 + 0.18 + 0.25
P(X < 5) = 0.54
b) The probability that the number of members in a typical household in India is greater or equal to 5 is given as:
P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8)
P(X ≥ 5) = 0.20 + 0.12 + 0.08 + 0.06
P(X ≥ 5) = 0.46
c) The the probability that the number of members in a typical household in India is strictly between 2 and 5
P(2 < X < 5) = P(X=3) + P(X=4)
P (2 < X < 5) = 0.18 + 0.25
P (2 < X < 5) = 0.43
Hence the probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively
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