A Road Safety Measure is Being Considered as an Intervention at a Site: Quantitative Methods Statistics Assignment, NUS, Singapore

Assignment Questions:

Question 1

A road safety measure is being considered as an intervention at a site where the long-term mean frequency of injury accidents is reckoned to be 4 per year. Calculate the range of numbers of accidents occurring during a 3-year monitoring period that will indicate that this measure is effective.

Question 2

When an independent sample of observations x = {x1, x2, x3, x4, ……..xn} has been made, the joint log-likelihood l (θ | x) of the parameters θ is calculated from the probability density function p (x | θ) according to the formula l (θ | X)= Σi=(1, n) logé p (xi | θ). Show that the log-likelihood for the parameter λ of an exponential distribution is maximized by setting it to the reciprocal of the sample mean: λ∗= 1/χ¯.