Question

x 20 The lifetime, in years, of a certain type of pump is a random variable with probability density function 3 (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

3 Here fons (14159 27,0 TRUE, lants more that 3 that 3 years ① Probability pump dra 2 3 (2+1)" 오 64 Somero [scana-- [com 2-[-] Probability lents betmen li hanya tina - - -- n' I to 2 yean 23 33 는 ta 216 2 27 32 (1) mean a E (2) 20125 sa Ý:30 2.3 مه 2 do = t 122+1 (x+134 (34 +234 [ put uza.

ECX) = 5 8 3x2 .dk (N=134 6 varsieme H-103 ③ climeilatue der finition F(+)2 f'(x) = 16 Is density (x+1)3- Now if median 2 q the 0.52 se ambje da - [65]? - [lewa - 1 +1 2 (2+1) 3 -0.5 (lauj - 29 Hlav (2+1)3 (2+1) = 2 21 2 2 272 (2+1) 92 24212012999 (approx). 2-1 = 0,2599 meads medran ? ② for 70'th percentile, 270, pereentily +1 70 100 =(18382 (2+1)3 30 2 21 100 (2+1) (ar) 320 21 21 (2+1) 2 1973 2269972,