This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 t 80 x 1 / 2 , x 80 , t 80 x. a. [ 8 marks ] Calculate 10  25 q 30 . b. [ 12 marks ] Obtain an expression for the corresponding force of mortality. Question 3 [20 marks] or the Poisson distributed random variable X (where Pr( X = x ) = e x /x !, for x = 0 , 1 , 2 , . . . ), derive a. [ 7 marks ] its mean, and b. [ 13 marks ] its variance. 1 Question 4 [40 marks] Let X n be the number of positive integers with n digits in which no two adjacent digits are the same. Some authors call this property redness . a. [ 8 marks ] Give an expression for X n . We are now going to derive an expression for the number of even red numbers. Let Y n be the number of even red numbers with n digits. b. [ 8 marks ] Derive a recursive equation relating Y n 1 to Y n . (A diagram may be useful.) c. [ 24 marks ] Solve your recursive equation in b above to show Y n = 9 n + ( 1) n 2 . End of paper 2...
View
Full
Document
 Three '10
 BernartWong

Click to edit the document details