please do both questions and details all steps ! please make it easy to follow

Question \#1: Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let x1,x2,x3 denote the lifetimes of components 1,2 , and 3 , respectively. Suppose the x 's are independent of one another and each x has an exponential distribution with parameter . a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to obtain the pdf. [Hint: F(y)=P(Yy); express the event {Yy} in terms of unions and/or intersections of the three events {X1y},{X2y}, and {X3y} ] b) Compute the expected system lifetime. Question \#2: An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X= the number of points earned on the first part and Y= the number of points eamed on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table. a) If the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score E(X+Y) ? b) If the maximum of the two scores is recorded, what is the expected recorded score