Question

The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (x+1) 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find the median lifetime. 7) Find the 70.-th percentile of the lifetime. Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.

Answer 1

Question ; otherwise 64 2 Auswer 2 2 (2) PR (1<x<2) f(x) da da - 19 216 8 27 pidet, f(x) =/(x+34 ; x 30 09– 8 (423) Li Brod le de = 3 [84*) (Tom) - 6 1,874 {{4413 )= (+b) fx fau.de cantida = 3 flex+1- 3 [(x4)*7*-*(649*) = 3 [ords Best I [1] -1 [1] Ausher (3) E(x) = da = 3 da. ( da (3+1)3 2*4134 - 3 (34+114 = 3/(1+1) 3-1 = Z - = 2 • Answer

(4)- E(X²)= fant 29.des for Ver *' J due da = 3 21+1)(x-1) dx + 3 da = 3 3 (31-1) dat 3 (21+13 (2+1)4 co (4+1-2) dx+3 dac xp = 3 da (4+1)2 +3 de (4+1)4 (21+1) 3 |(>1+114 (4+)3 co + = 3 (2013) *-- (694) * ] s (68"*I ---- 9 = 3(1)-3(1) + (1) = | VAL. (x)= F(x2- [Ex}} = 1-4)=:-* - 4 - Answer