Let X1,X2,X3,X4 be observations of a random sample of n-4 from the exponential distribution having mean...

Question

Question

Let X1,X2,X3,X4 be observations of a random sample of n-4 from the exponential distribution having mean 5, What is the mgf of

Answer 1

Answer #1

The solution to this problem is given below-

Given , x , X₂ X₃ X4 d exp(s). . The PDF of Xi is a f(xi), se 5*, xde. : MGF ob Xi, (i=1(14) Mx; <t) - ef Elet*;), teir ſetki

- Elett) Elette) Eletxs) E (Beta) TX, X₂ X₃ X4 are independent to each other] - 54 6-t-4 which is the MGF of Gamma (455) (5)

MGF ob is (5)* <4) Now, from the Uniqueness property of MGF we can say X~ Gamma (4,20). .: The PDF of xis, f(a)- 201 (3)te-5

Answer 2

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