A study of the noise level on takeoff of jets at a particula

A study of the noise level on takeoff of jets at a particularairport is studied. The random variable is X, the noise in decibels of the jet as it passes over the first residential area adjacent to the airport. This random variable is assumed to have a gamma distribution with alpha = 2 and beta unknown.

(a) Find the maximum likelihood estimate for beta based on a sample of size n.

(b) Use beta-hat to find an estimate for the mean value of X. Is this estimator unbiased for u (mu)?

(c) Find the maximum likelihood estimate for beta based on these data:

55 65 60 73 80

64 57 75 62 86

69 100 70 82 65

72 67 61 95 52

(d) Estimate the average decibel reading of these jets.

ANSWER: (a) b-hat = x-bar/2 (c) 35.25 (d) 70.5

Solution