Question
Asked Oct 29, 2019
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1. Given that yı = 3.2, y2 = 1.3, y3 = 4.1 is a random sample from
yeu/o
fr (y;0)=
604
y 20,
calculate the maximum likelihood estimate for 0.
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1. Given that yı = 3.2, y2 = 1.3, y3 = 4.1 is a random sample from yeu/o fr (y;0)= 604 y 20, calculate the maximum likelihood estimate for 0.

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Expert Answer

Step 1

Given data

= 3.2, y2 1.3, y3 =
1.3, Уз
= 4.1
y
ев
fyy: 0)
11
604
Likelihood function is given by
п
L(),: 0)
O:0)
i=1
n
-y1
y2
— Уп
3
ө
узе в
ује в
X ... ... X
604
604
604
604
i=1
-i=1& |=1 Yi
е
,3
(604)n
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= 3.2, y2 1.3, y3 = 1.3, Уз = 4.1 y ев fyy: 0) 11 604 Likelihood function is given by п L(),: 0) O:0) i=1 n -y1 y2 — Уп 3 ө узе в ује в X ... ... X 604 604 604 604 i=1 -i=1& |=1 Yi е ,3 (604)n

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Step 2

Taking natural Log...

- Σ
In L (e) In
(604)n
yi-In(604)"
=> In e 2i=19
i=1
n
Σ
yi
n ln 604
i=1
Taking the derivative and equating it to zero
a In L(e)
0
дө
Σ
1
п
x 2403 0
604
yi 0
02
Σ
x 2403
604
=>
ө2
У
Σν
3.2 1.34.1
0.7167
4n
4 x 3
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- Σ In L (e) In (604)n yi-In(604)" => In e 2i=19 i=1 n Σ yi n ln 604 i=1 Taking the derivative and equating it to zero a In L(e) 0 дө Σ 1 п x 2403 0 604 yi 0 02 Σ x 2403 604 => ө2 У Σν 3.2 1.34.1 0.7167 4n 4 x 3

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