Question 35. Let X be a random variable defined by the density function if x > B f(x) = xa+1 else with parameters a > 0 and ß > 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 B. b) The expected value does only depend on a, but not on B. c) Given the sample, B can not be larger than 3. 5 d) If we assume B = 2, the estimation of the expected value from the sample mean leads to an estimate of for 3 α. 5 is also the maximum likelihood estimate of a in this case. 3

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Question 35. Let X be a random variable defined by the density function
if ε β
f(x) =
xa+1
else
with parameters a > 0 andB > 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 ß.
b) The expected value does only depend on a, but not on B.
c) Given the sample, B can not be larger than 3.
5
d) If we assume 3 = 2, the estimation of the expected value from the sample mean leads to an estimate of
for
3
a.
5
e)
is also the maximum likelihood estimate of a in this case.
3
Transcribed Image Text:Question 35. Let X be a random variable defined by the density function if ε β f(x) = xa+1 else with parameters a > 0 andB > 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 ß. b) The expected value does only depend on a, but not on B. c) Given the sample, B can not be larger than 3. 5 d) If we assume 3 = 2, the estimation of the expected value from the sample mean leads to an estimate of for 3 a. 5 e) is also the maximum likelihood estimate of a in this case. 3
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