- #1

- 5

- 0

## Homework Statement

During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10 miles. A certain county is responsible for repairing potholes in a 30 mile stretch of the interstate. Let X denote the number of potholes the county will have to repair at the end of next winter.

1. The random variable X is

(i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson

2. Give the expected value and variance of X.

3. The cost of repairing a pothole is $ 5000. If Y denotes the county's pothole repair expense for next winter,find the mean value and variance of Y ?

## Homework Equations

and Attempt at a solution1.) Pretty sure this is a Poisson random variable

2.) P = ([itex]\alpha[/itex]

^{x}* e

^{-[itex]\alpha[/itex]})/ x!

In this case [itex]\alpha[/itex] = 0.16 potholes/mile

x represents 0, 1, 2, ... , 30 is this correct?

Expected value of X= [itex]\alpha[/itex] = 0.16 potholes/mile

Variance of X = expected value of X = [itex]\alpha[/itex] = 0.16 potholes/mile

Y = aX + b

X = potholes that need to be fixed

a = 5000 (cost to fix each pothole)

b = 0

Expected value of Y = a * Expected value of X

Variance of Y = a

^{2}* Variance of X