4. Drawing Batteries I You have an endless box of used batteries. Assume that the number of hours remaining in a battery is i.i.d., uniformly distributed on [O 1 l]. (a.) Suppose you draw 7; batteries. Suppose that the ith battery you draw has Xi hours remaining. What is P(X1 S X2 S . . . g Xn )? Now, you draw batteries until you have enough batteries to last one hour. Let N be the number of batteries you draw. (b) What is P(X1+ X2 S 1)? What about P(X1+ X2 + X3 S 1)? (0.) Find the distribution and expectation of N. Hint: Try to relateP(X1+ X2 + - - -+ XN S 1) to the quantity you found in part a