1

COLUMBIA UNIVERSITY
DEPARTMENT OF BIOSTATISTICS
P8109 – STATISTICAL INFERENCE
MIDTERM EXAMINATIONS - SPRING 2020

INSTRUCTIONS:
 Time allowed: 60 minutes
 Answer ALL questions.



Question 1
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]

Question 2
A sample 1,..., nY Y is drawn from a gamma distribution with parameters 0 (known) and
 (unknown):
 
 
0
0
1 /
0
,
0
i
y
Y
y e
f y y
 
 
 
 


Obtain a sufficient statistic for 


[8 marks]


Dr P Gorroochurn 3/27/2020



















































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