During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10miles. A certain county is responsible for repairing potho
les in a 30-mile stretch of the interstate. LetXdenote the number of potholes thecounty will have to repair at the end of next winter. (a) The distribution of the random variable X is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Give the expected value and variance of X.
(c)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 Y?
We can appropiately describe this random variable with a Poisson distribution, as the probability of having a pothole can be expressed as a constant rate per mile (0.16 potholes/mile) multiplied by the stretch that correspond to the county (30 miles).
The parameter of the Poisson distribution is then:
b) The expected value and variance of X are both equal to the parameter λ=4.8.
The answer is -2. The line is going from left to right which makes it negative. Then if you look at the line and do change in y(rise) over change in x(run).
The angle of depression is the same as the base angle next to the right angle because of alternate interior angles. Use the tangent ratio: . The angle of depression, therefore, is 27