Question

A seal on a brand of pump will fail eventually due to leakage, and the time to failure for a given seal can be viewed as a random variable X. Evidence has shown that the time to failure of the seal can be modelled via an exponential distribution. Additionally, 20% of seals on this brand of pump fail within the first 2 years. (a) What value of A should be used in modelling X exp(4)? (4 marks] (b) What is the probability that the seal from a pump of this brand lasts at least 5 years? (3 marks) (c) If a seal from a pump of this brand has lasted 3 years without failure, what is the probability that it lasts at least 5 more years? (3 marks

Answer 1

Solution: Given 'dala: brand of Pump will fail eventually due to leakage, Let a) mean of the distribustion be 1 Then x~ exp (x) and PDF is - fx (x) P(x= x) =xe λχ and CDF iss Fy(x) > p (x4x) 1--23 we are given that 20t. seals fail within figst 2 years. p (+52)=0-2 SO, fx (2) = 1- e ax -02 -22 0.8

a -2x ) In (0.8) -In (0.8) 2 ০ 2x 0.1116 year AS 01/16 so, 2 yo exp (0.1116) real would least so, probability that the least year at 5 (SE p (425) = -PCX45) = 1 - Fy (5) =l-FX (5) sl-(1-7X(5)) E (0.1116) X5 0.5724

c) as exponential distribution 3 es a nicmory less distribution, som p( xs x+y) x= x) = P(xzy) p(x33 +51 X23) - P (*25) So, 6.5724 please give me thumb up