Description
1. (5 points) Suppose on flipping an unbiased coin we observe 0, 1, 1, 0, 0, 1, 1, 0, 0, 1.
(a) Calculate the estimate of the unknown parameter using method of moments.
(b) Find the maximum likelihood estimate of the unknown parameter.
(c) Obtain the maximum likelihood estimate in R.
(d) Compare the estimates obtained by the above methods.
2. (5 points) The following data are the number of days it took for rats painted with
a carcinogen to develop carcinoma
143, 164, 188, 188, 190, 192, 206, 209, 213, 216, 220, 227, 230, 246, 265, 304, 234.
Suppose the data could be modeled as Weibull (c, σ) distribution. The pdf is given
by
fc,σ(x) = c
σ
x
σ
c−1
e
−(x/σ)
c
, x > 0, c > 0, σ > 0.
(a) Derive the maximum likelihood estimator (MLE) of (c, σ).
(b) Construct a code in R to get the maximum likelihood estimate of the unknown
parameters for the data.
3. (5 points) Question 7.28 from Statistical Inference by Casella and Berger (2nd
Edition).
