, if æ > B S(x) = else parameters a >0 and 8 > 0. We observe a sample {3,4, 8}. Which of the The expected value of X exists for all combinations of a and B. The expected value does only depend on a, but not on 3. Given the sample, 3 can not be larger than 3. If we assume 3 = 2, the estimation of the expected value from the sample a. 5 is also the maximum likelihood estimate of a in this case.

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ISBN:9781119256830
Author:Amos Gilat
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Question 35. Let X be a random variable defined by the density function
if r 2 3
f(r) = { ra+1
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 3.
c) Given the sample, 3 can not be larger than 3.
d) If we assume 3 = 2, the estimation of the expected value from the sample mean leads to an estimate of
for
a.
e)
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 r 2 3 f(r) = { ra+1 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 3. c) Given the sample, 3 can not be larger than 3. d) If we assume 3 = 2, the estimation of the expected value from the sample mean leads to an estimate of for a. e) is also the maximum likelihood estimate of a in this case.
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