2.7 The Itwill Fail Company manufactures gizmos for use on widgets. The time to failure, in years, of these gizmos has the following PDF: f(x)= 200 (+10)³ for ≥0 (a) Derive the reliability function and determine the reliability for the first year of op- eration. (b) Compute the MTTF. (c) What is the design life for a reliability of 0.95? (d) Is the failure rate DFR, CFR, or IFR? (e) Will a one-year burn-in period improve the reliability in part (a)? If so, what is the new reliability?