Heres the question, i been working on it for a while but i cant seem to get it rite..please help!
1. A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to the difference between the radius of the hole and the radius of the shaft. Let the random variable X denote the clearance, in millimeters. The probability density function of X is
f(x) = 1.5(1-x^4) 0<x<1
Components with clearances larger than 0.8 mm must be scrapped. What proportion of components are scrapped?
Find the mean clearance.
2. Find the solution of the differential equation xy' + y = y^2that satisfies the initial condition of y(1)= -1