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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 mor-tality. 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...
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- Three '10