T1-S-232-2010W

# T1-S-232-2010W - SOLUTIONS TO TUTORIAL 1 ACTSC 232 WINTER...

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

SOLUTIONS TO TUTORIAL 1 - ACTSC 232, WINTER 2010 1. (a) S 0 ( x ) = e - R x 0 μ t dt = (1 - x 100 ) 2 for 0 x < 100 and S 0 ( x ) = 0 for x 100. (b) The probability is Pr { 10 < T 30 < 30 } = S 30 (10) - S 30 (30) = S 0 (40) - S 0 (60) S 0 (30) = 0 . 4082. (c) We have t p x = S 0 ( x + t ) S 0 ( x ) = ( 100 - x - t 100 - x ) 2 for 0 t 100 - x and t p x = 0 for t > 100 - x . (d) f 30 ( t ) = t p 30 μ 30+ t = (70 - t ) / 2450 , 0 t < 70. (e) E [ T 30 ] = R 0 t p 30 dt = R 70 0 ( 70 - t 70 ) 2 dt = 70 / 3 or E [ T 30 ] = R 0 tf 30 ( t ) dt = R 70 0 t (70 - t ) 2450 dt = 70 / 3. (f) We have E [ K 30 ] = k =1 k p 30 = 70 k =1 (1 - k 70 ) 2 = 22 . 84 . (g) Pr { K 30 = 20 } = 20 p 30 - 21 p 30 = 0 . 0202 . (h) Pr { K 30 < 30 } = Pr { T 30 < 30 } = 30 q 30 = 0 . 6735 . (i) Pr { K 30 40 } = Pr { T 30 < 41 } = 41 q 30 = 0 . 8284 . 2. We are given that 0 . 02 = q x = 1 - p x = 1 - e - R 1 0 μ x + t dt and 0 . 04 = q x = 1 - p x = 1 - e - R 1 0 ( μ x + t + c ) dt . Hence, c = ln 98 96 . 3. Note that 0

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.

{[ snackBarMessage ]}

### Page1 / 2

T1-S-232-2010W - SOLUTIONS TO TUTORIAL 1 ACTSC 232 WINTER...

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

View Full Document
Ask a homework question - tutors are online