9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density function given by -|()** ye-3/0 y > 0, otherwise. That is, Y has a gamma distribution with parameters a = 2 and 0. Letê denote the MLE of 9. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. f(x|0)= a Find the MLE of 0. b Find E (0) and V (8). c Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What is the MLE for the variance of Y?

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9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density
function given by
f(y|0)= { (1)
y> 0,
otherwise.
That is, y has a gamma distribution with parameters α = 2 and 0. Let Ô denote the MLE of
8. Suppose that three such components, tested independently, had lifetimes of 120, 130, and
128 hours.
a
Find the MLE of 0.
b Find E() and V (8).
c
82 ye-3/0
Suppose that actually equals 130. Give an approximate bound that you might expect for
the error of estimation.
d What is the MLE for the variance of Y?
Transcribed Image Text:9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density function given by f(y|0)= { (1) y> 0, otherwise. That is, y has a gamma distribution with parameters α = 2 and 0. Let Ô denote the MLE of 8. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of 0. b Find E() and V (8). c 82 ye-3/0 Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What is the MLE for the variance of Y?
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