Question: 89. Some components of a two-component system fail after receiving a shock. Shocks of three types arrive independently and in accordance with Poisson processes. Shocks

89. Some components of a two-component system fail after receiving a shock. Shocks of three types arrive independently and in accordance with Poisson processes. Shocks of the first type arrive at a Poisson rate and cause the first component to fail. Those of the second type arrive at a Poisson rate and cause the second component to fail. The third type of shock arrives at a Poisson rate and causes both components to fail. Let and denote the survival times for the two components. Show that the joint distribution of and is given by This distribution is known as the bivariate exponential distribution.

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