Question

Assume that the probability that a person is killed by coronavirus in a year is, independently, 1/(200 million). Assume that the TR population is 100 million. (5 poi. for each parts)

a. Compute P(3 or more people will be killed by coronavirus next year) exactly.

b. Approximate the probability that found in (a).

c. Approximate the probability that ONO or more people are killed by coronavirus within the first 3 months of next year.

d. Approximate the probability that in exactly 3 of next 10 years exactly 4 people are killed by coronavirus. e. Find the expected number of years, among the next 5, in which 2 or more people are killed by coronavirus.

Answer 1

Question 2.

(a) Here probability that a person is killed by coronavirus in a given year is 1/200 million.

TR population = 100 million

so expected number of persons to be killed in next year = 100/200 = 0.5

so here if x is the number of person to be killed by coronavirus next year, then

x ~ BINOMIAL (n = 100 milion, p = 1/200 million)

P(x >= 3) = 1 - BINOMDIST(x < 3; n = 100 milion, p = 1/200 million)

=1 - 0.9856 = 0.0144

(b) Now approximating it with poisson distribution

x ~ POISSON (0.5)

P(3 or more people will be killed by coronavirus) = 1 - POISSON (x < 5; 0.5) = 1- 0.9856 = 0.0144

(c) Expectd number of deaths in 3 months = 3/12 * 0.5 = 0.125

P(x >= 1) = 1- POISSON(x < 1 ; 0.125) = 1- 0.8825 = 0.1175

(d) P(4 people are killed in a given year) = e^-0.5 0.5⁴/4! = 0.0016

if y is the number of years whe exactly 4 people has died then y ~ BINOMIAL (n = 10, p = 0.0016)

P(y = 3) = BINOMDIST(y = 3; n = 10; p = 0.0016; false) = 4.68 x 10^-7

(e) P(x >=2) = 1 - POISSON(x < 2; true) = 1 - 0.9098 = 0.0902

expected number of years amog next 5 years = 0.0902 * 5 = 0.45 years