Two companies, Company 1 and Company 2, have just been founded. Stock market crashes
Chapter 7, Problem 25(choose chapter or problem)
Two companies, Company 1 and Company 2, have just been founded. Stock market crashes occur according to a Poisson process with rate 0. Such a crash would put both companies out of business. For j 2 {1, 2}, there may be an adverse event of type j, which puts Company j out of business (if it is not already out of business) but does not aect the other company; such events occur according to a Poisson process with rate j . If there has not been a stock market crash or an adverse event of type j, then company j remains in business. The three Poisson processes are independent of each other. Let X1 and X2 be how long Company 1 and Company 2 stay in business, respectively. (a) Find the marginal distributions of X1 and X2. (b) Find P(X1 > x1, X2 > x2), and use this to find the joint CDF of X1 and X2.
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