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Asked Oct 29, 2019
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2. Use the method of maximum likelihood to estimate 0 in the pdf
V, y0.
fr (y; 0)
2/y
Evaluate 0e for the following random sample of size 4: yi 6, y2 = 8, y3 = 2.4, y4 = 5.9.
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2. Use the method of maximum likelihood to estimate 0 in the pdf V, y0. fr (y; 0) 2/y Evaluate 0e for the following random sample of size 4: yi 6, y2 = 8, y3 = 2.4, y4 = 5.9.

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Expert Answer

Step 1

Given data

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6, y2 8,y3 2.4, y4 = 5.9 y Өе -ву fy(y; 0) 2y Likelihood function is given by п IH50:0) L(0) i=1 e- 2/y п Өе-в\Ух Ѳе-ө\уз Өе-ву х Өе-в/ул ө = X х 2/y1 2 2 2y3 2/yn i=1 D

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Step 2

Taking natural Log...

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n In L (e) In 2. Л-1Уi ө 1 Vyi -In 2 Ө => n ln yi 2 i=1 i-1 Taking the derivative and equating it to zero a In L(e) 0 дө n ->i-0= 0 /2 i 1 n 2n Σσ e i-1 2n => e =1Vyi 2 X 4 Ө V682.4 5.9 0.86429 D

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