Question

Stanley is looking to retire and move near the ocean. The Jersey Shore has seen a rise in sea levels the past few years. These high tides have caused floods in 100 places that call themselves Jersey Shore towns, which are on or within reasonable distance of the ocean. Stanley is nervous about possible floods and would like to be prepared for costs associated with them. As Stanley’s friend and an expert in risk management, you collect past information and have constructed the following probability distribution for the number of floods per town per summer at the Jersey Shore. # of floods per town per summer Probability 0 0.10 1 0.15 2 0.26 3 0.30 4 0.15 5 0.04 a. Calculate the expected frequency of floods per town per summer. (2 points) b. Calculated the variance. (2 points)

Answer 1

2.37 ; 1.6731

Explanation:

Given the data:

X:___0____1____2____3____4____5

P(x):_0.10_0.15_0.26__0.30_0.15__0.04

the expected frequency of floods per town per summer

Σ(flood per Town per summer) * probability

Σ(X)*p(x)

Σ(0*0.10) + (1*0.15) + (2*0.26) + (3*0.30) + (4*0.15) + (5*0.04)

= (0 + 0.15 + 0.52 + 0.90 + 0.60 + 0.2)

= 2.37

Variance (s²) :

Σ[x². P(x)] - u²

Using an online variance calculator to save computation time :

s² = 16731 / 10000

s² = 1.6731