Consider a system comprising four components (A, B, C and D) connected as in the figure below. A B C D The system is working if there is a path through working components from left to right. Suppose that components fail independently and the time to failure for each component has an exponential distribution with a mean of two years. Let T denote the time of failure for the system. Determine an expression for the probability that the system is working at time t, that is P(T > t). Hence, give the probability density function for the time to failure of the system. Also Determine the mean, variance and moment generating function of the time to failure for the system. Consider a system comprising four components (A, B, C and D) connected as in the figure below. A B C D The system is working if there is a path through working components from left to right. Suppose that components fail independently and the time to failure for each component has an exponential distribution with a mean of two years. Let T denote the time of failure for the system. Determine an expression for the probability that the system is working at time t, that is P(T > t). Hence, give the probability density function for the time to failure of the system. Also Determine the mean, variance and moment generating function of the time to failure for the system