DEPARTMENT OF BIOSTATISTICS
P8109 – STATISTICAL INFERENCE
MIDTERM EXAMINATIONS - SPRING 2020
Time allowed: 60 minutes
Answer ALL questions.
Let X and Y be independent r.v.’s, each with a normal distribution, such that EX
E 3Y , var X = var Y = 1.
(a) Find the MLE of .
(b) If an estimator of the form aX + bY is to be used to estimate , what restrictions
must the constants a and b satisfy in order that the estimator be unbiased?
[8+4 =12 marks]
A sample 1,..., nY Y is drawn from a gamma distribution with parameters 0 (known) and
f y y
Obtain a sufficient statistic for
Dr P Gorroochurn 3/27/2020 学霸联盟