An engineer states that the error X in a measurement has probability distribution in the following form: at): 2(1+A+:c} forlAEIEl, =h for1Ezgl, h =X(1+A I) for1m51+A =Uelsewhere. 1 Note that A > U. (a) First, plot 3" (:12) Then, nd the factor it (in terms of A), which will make f(l') a proper probability density function. (Hint: From the shape of x), you will notice that there is a simpler way to do this than integrating.) [5 pts.] {b} What is the expected value of X 7 [3 pts. ] {c} If A 1. 6 what 1s the value of X at the 75th percentile (i. e. X0 75)? (Hint: start by assuming that Xars S 1) [3 PtE-l