To investigate the wind speed X at CUHK, one hundred observations, #1, x2, ..., ¤100, on X are recorded. On theoretical ground, it is postulated that the probability density function (PDF) of the wind speed at CUHK is f(r; 3) = { 23ze-ße", for æ > 0 0, otherwise where B > 0 is an unknown parameter. (a) Suppose that n observation, X1, X2, ..., X, (not all zeros), constitute a random sample from the distribution f(x; B). Determine the maximum-likelihood estimator

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To investigate the wind speed X at CUHK, one hundred observations, r1, T2, ..., T100;
on X are recorded. On theoretical ground, it is postulated that the probability density
function (PDF) of the wind speed at CUHK is
f(r; ß) = { 0,
[ 23re-Ba², for r > 0
otherwise
where B > 0 is an unknown parameter.
(a) Suppose that n observation, X1, X2, . .., X, (not all zeros), constitute a random
sample from the distribution f(x; 3). Determine the maximum-likelihood estimator
of 3.
(b) Given that E a? = 800. Determine an approximate 90% confidence interval
for 3.
Consider the details provided in Question 1 again.
(a)) Determine the cumulative density function (CDF) F(x; B) of X for all
-00 <x < 0o.
Transcribed Image Text:To investigate the wind speed X at CUHK, one hundred observations, r1, T2, ..., T100; on X are recorded. On theoretical ground, it is postulated that the probability density function (PDF) of the wind speed at CUHK is f(r; ß) = { 0, [ 23re-Ba², for r > 0 otherwise where B > 0 is an unknown parameter. (a) Suppose that n observation, X1, X2, . .., X, (not all zeros), constitute a random sample from the distribution f(x; 3). Determine the maximum-likelihood estimator of 3. (b) Given that E a? = 800. Determine an approximate 90% confidence interval for 3. Consider the details provided in Question 1 again. (a)) Determine the cumulative density function (CDF) F(x; B) of X for all -00 <x < 0o.
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