Consider the system comprised of three components as shown below. Suppose each component i has a lifetime that is distributed independently as an Exponential distribution with parameterX₁, where lambda₁ = 1/10, lambda2 =1/ 20 and lambda3 =1/15. In other words, the system is working if both• component 1 is working, and• at least one of components 2 and 3 is working. (a) (4 points) Let r; be the probability that component i is still working at time t = 6. Find rį for i = 1, 2, 3. (b) (4 points) Compute the probability that the system is still working at time t = 6. Justify your steps. (State your answer in terms of r; if you are unable to solve part (a).)

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