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 Equationsand Attempt at a solution
1.) 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 = a2 * Variance of X