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Probability - Random variables

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data

    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 ?

    2. Relevant equations and 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
     
  2. jcsd
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