Suppose that we have two bonds A and B. Denote by T_A and T_B their respective default times (in year). Suppose that T_A follows exponential distribution with hazard lambda_A = 0.01 (i.e. P(T_A greaterthanorequalto t) = e^-lambdaAt) and T_B follows exponential with hazard lambda_B = 0.02. Suppose that jointly they satisfy the Gumbel copula with alpha = 2. Find the probabilities that (i) both will default by the end of the first year; (ii) at least one will default by the end of the first year. Suppose that we have two bonds A and B. Denote by T_A and T_B their respective default times (in year). Suppose that T_A follows exponential distribution with hazard lambda_A = 0.01 (i.e. P(T_A greaterthanorequalto t) = e^-lambdaAt) and T_B follows exponential with hazard lambda_B = 0.02. Suppose that jointly they satisfy the Gumbel copula with alpha = 2. Find the probabilities that (i) both will default by the end of the first year; (ii) at least one will default by the end of the first year