1. (BH 7.25) 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 E {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 affect the other company; such events occur according to a Poisson process with rate A,. 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 X 1 and X2 be how long Company 1 and Company 2 stay in business, respectively. (a) Find the marginaldistributionsof X1 and X2. (b) Find P(Xl >1131,X2 >552), and use this to find thejoint CDF of X1 and X2