Assignment2 Solution

# Assignment2 Solution - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II(2010-11

This preview shows pages 1–2. Sign up to view the full content.

DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II (2010-11) Assignment 2 suggested solutions 1. (a) i. Observed data: number of marked ﬁsh in recaptured load x = x = 100. ii. Parameter: θ = N ∈ { 2900 , 2901 ,... } . iii. Likelihood function: ( θ ) = ( 1000 100 )( N - 1000 1900 ) ( N 2000 ) . (b) i. Observed data: number of heads turned up x = x = 60. ii. Parameter: θ = p [0 , 1]. iii. Likelihood function: ( θ ) = ( 100 60 ) p 60 (1 - p ) 40 . (c) i. Observed data: interarrival times of customers x = ( x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ) = (8 , 4 , 3 , 8 , 6 , 1). ii. Parameter: θ (0 , ). iii. Likelihood function: ( θ ) = θ 5 e - θ 5 i =1 x i e - θx 6 = θ 5 e - 30 θ . (d) i. Observed data: number of patients receive ordinary and new treatments x = ( x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ) = (12 , 6 , 36 , 18 , 12 , 24). ii. Parameter: θ = ( p s ,p m ,p n ,q s ,q m ,q n ) [0 , 1] 6 , p = q = 1. iii. Likelihood function: ( θ ) = 54! 12!6!36! p 12 s p 6 m p 36 n 54! 18!12!24! q 18 s q 12 m q 24 n . (e) i. Observed data: number of bus breakdowns x = x = 3. ii. Parameter: θ = λ (0 , ). iii. Likelihood function: ( θ ) = λ 3 e - λ 3! = λ 3 e - λ 6 . (f) i. Observed data: heights of students x = ( x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ,x 7 ,x 8 ,x 9 ) = (1 . 72 , 1 . 76 , 1 . 80 , 1 . 65 , 1 . 56 , 1 . 48 , 1 . 62 , 1 . 55 , 1 . 58). ii. Parameter: θ = ( μ 1 2 1 2 ) R 2 (0 , ) 2 . iii. Likelihood function: ( θ ) = 1 ( 2 πσ 1 ) 4 exp ± - 4 i =1 ( x i - μ 1 ) 2 2 σ 2 1 ² 1 ( 2 πσ 2 ) 5 exp ± - 9 i =5 ( x i - μ 2 ) 2 2 σ 2 2 ² = 1 ( 2 π ) 9 σ 4 1 σ 5 2 exp - 12 . 0185 - 13 . 86 μ 1 + 4 μ 2 1 2 σ 2 1 - 12 . 1473 - 15 . 58 μ 2 + 5 μ 2 2 2 σ 2 2 ³ . (g) i. Observed data: number of male x = x = 1. ii. Parameter: θ = m ∈ { 1 , 2 ,..., 1996 } . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/17/2011 for the course MUSIC 1001 taught by Professor Dr.yun during the Spring '11 term at Princess Sumaya University for Technology.

### Page1 / 6

Assignment2 Solution - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II(2010-11

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online