1. A bank has three loans, denoted by L1,L2 and L3. Each loan may or may not be default in 2023 and they are independent each other about the default or no default. Suppose the probability of default for L1,L2 or L3, respectively, is equal to 0.1,0.2 and 0.3 if the economy is not in recession in 2023, or 0.2,0.3,0.4 if the economy is in recession in 2023. Find the probability of at MOST one loan is default in 2023. 2. For Problem 1 with no recession happens in 2023, define the random variable for each i, Xi(Li)={1,0,iftheloanLiisdefaultiftheloanLiisnodefault. Let X=X1+X2+X3. Find E[X] and Var(X) 1. A bank has three loans, denoted by L1,L2 and L3. Each loan may or may not be default in 2023 and they are independent each other about the default or no default. Suppose the probability of default for L1,L2 or L3, respectively, is equal to 0.1,0.2 and 0.3 if the economy is not in recession in 2023, or 0.2,0.3,0.4 if the economy is in recession in 2023. Find the probability of at MOST one loan is default in 2023. 2. For Problem 1 with no recession happens in 2023, define the random variable for each i, Xi(Li)={1,0,iftheloanLiisdefaultiftheloanLiisnodefault. Let X=X1+X2+X3. Find E[X] and Var(X)