Answer to Question #308112 in Statistics and Probability for Peter

Question

In the year 1918 a flu like disease occurred in Spain and spread to the rest of the world. This year 2020 another similar flu like disease has occurred in china and is spreading in the whole world. Researchers have found that the likelihood of the disease occurring again is 0.01.Determine the average number of flus in the next 300 years and the likelihood that in the next 300 years, the disease will occur at most five times.       

Answer 1

We define the following

The likelihood of the disease occurring again is, p =  0.01.

Number of years in consideration, n = 300

Average number of flus in the next 300 years = np = 300 * 0.01 = 3

As, n is large , p is small and np < 5, the number of occurrence of the disease in next 300 years can be modeled by Poisson distribution with mean parameter  = 3 per 300 years.

Let X be the number of occurrence of the disease in next 300 years.

X ~ Poisson( = 3)

The likelihood that in the next 300 years, the disease will occur at most five times = P(X$\leq$   5)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

= exp(-3) * 3⁰ / 0! + exp(-3) * 3¹ / 1! + exp(-3) * 3² ​​​​​​​/ 2! + exp(-3) * 3³​​​​​​​/ 3! + exp(-3) * 3⁴ ​​​​​​​/ 4! + exp(-3) * 3⁵ ​​​​​​​/ 5!

= 0.04978707 + 0.14936121 + 0.22404181 + 0.22404181 + 0.16803136 + 0.10081881

= 0.9160821