Question 35. Let X be a random variable defined by the density function aga f(r) ={a+1 , if a2B else with parameters a >0 and 8 > 0. We observe a sample {3,4,8}. Which of the following statements are correct? a) The expected value of X exists for all combinations of a and 8. b) The expected value does only depend on a, but not on 3. c) Given the sample, 8 can not be larger than 3.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Question 35. Let X be a random variable defined by the density function
if a > 3
f(r)
else
with parameters a > 0 and 3 > 0. We observe a sample {3, 4, 8}. Which of the following statements are correct?
a) The expected value of X exists for all combinations of a and 3.
b) The expected value does only depend on a, but not on B.
c) Given the sample, 3 can not be larger than 3.
d) If we assume B = 2, the estimation of the expected value from the sample mean leads to an estimate of
for
a.
5
e)
3
is also the maximum likelihood estimate of a in this case.
Transcribed Image Text:Question 35. Let X be a random variable defined by the density function if a > 3 f(r) else with parameters a > 0 and 3 > 0. We observe a sample {3, 4, 8}. Which of the following statements are correct? a) The expected value of X exists for all combinations of a and 3. b) The expected value does only depend on a, but not on B. c) Given the sample, 3 can not be larger than 3. d) If we assume B = 2, the estimation of the expected value from the sample mean leads to an estimate of for a. 5 e) 3 is also the maximum likelihood estimate of a in this case.
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