8. Lifetime of certain device is exponentially distributed random variable T( 2 ), 2 = .1 Find the expectation and variance for this distribution. 1p The system consists of 5 devices of such type and is in working condition if all of its components are in working condition. What is the density function of random variable S, lifetime of system ? 2p What is cumulative function of random variable S ? Find the probability that system will not fail 3p a) in the first 2 years? b) in the next 2 years given that it didn't fail in the first 2years? c) If you have 6 such system, what is probability that at exactly 3 will not AP fail in the next 2 years