5. A strand of string of length L > 0 is cut into two pieces of lengths X and L - X. X follows a uniform distribution over the interval (0, L). Let Y be the length of the longer piece of string. (a) Find E (Y). (b) Find the cdf for Y. (c) Find the pdf for Y. (d) Compute P (Y - 17L 20 ly > 2 (e) Suppose the mass per unit length of the string is p. Find the expected mass for the shorter piece of string. Your answer should depend on p and L.5. A strand of string of length L > 0 is cut into two pieces of lengths X and L - X. X follows a uniform distribution over the interval (0, L). Let Y be the length of the longer piece of string. (a) Find E (Y). (b) Find the cdf for Y. (c) Find the pdf for Y. (d) Compute P (Y - 17L 20 ly > 2 (e) Suppose the mass per unit length of the string is p. Find the expected mass for the shorter piece of string. Your answer should depend on p and L