Losses come from a mixture of an exponential distribution with mean 100 with probability p and an exponential distribution with mean 10,000 with probability 1- p. Losses of 100 and 2000 are observed. Determine the likelihood function of p. -0.01 pe (1– p)e -20 pe0 (1– p)eº. -0.2 (A) 100 10,000 100 10,000 рe (1-р)e 001 -20 (1– p)eº -0.2 (В) pe 100 10,000 100 10,000 pe (1- p)e e 0.01 -20 pe 100 (1– p)e 02 (C) 100 10,000 10,000 pe (1- p)e -0.01 ре -20 ре - p)e (D) (1- -0.2 100 10,000 100 10,000 el p. 100 10,000 e0.01 +(1- p)| (E) -20 e e-0.2 100 10,000

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Losses come from a mixture of an exponential distribution with mean 100 with probability p
and an exponential distribution with mean 10,000 with probability 1- p.
Losses of 100 and 2000 are observed.
Determine the likelihood function of p.
0.01
pe' (1– p)e0«
(1– p)e 02
-20
-0.2
(A)
pe
100
10,000
100
10,000
-20 (1– p)e 02
ре (1- рје 001
10,000
(B)
ре
100
100
10,000
pe, (1- p)e 0.01)
20 (1– p)e02
(C)
ре
ре
100
10,000
100
10,000
Pel
100
(1– p)e-001
(1– p)e-02
-20
(D)
ре
10,000
100
10,000
e-0.2
+
100 10,000
e
e
0.01
-20
(E)
р.
+
100 10,000
Transcribed Image Text:Losses come from a mixture of an exponential distribution with mean 100 with probability p and an exponential distribution with mean 10,000 with probability 1- p. Losses of 100 and 2000 are observed. Determine the likelihood function of p. 0.01 pe' (1– p)e0« (1– p)e 02 -20 -0.2 (A) pe 100 10,000 100 10,000 -20 (1– p)e 02 ре (1- рје 001 10,000 (B) ре 100 100 10,000 pe, (1- p)e 0.01) 20 (1– p)e02 (C) ре ре 100 10,000 100 10,000 Pel 100 (1– p)e-001 (1– p)e-02 -20 (D) ре 10,000 100 10,000 e-0.2 + 100 10,000 e e 0.01 -20 (E) р. + 100 10,000
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