Problem 3: An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by f (x) = 10 3x -4 x> 1 elsewhere Find the mean particle size. Find the variance of X. Problem 4: Based on extensive testing, it is determined by the manufacturer of a washing machine that the time Y (in years) before a major repair is required is characterized by the probability density function f( y) = 0.25 e-y/4 y 20 0 , elsewhere (a) What is the probability that a major repair does not occur in the first year? (b) Find the mean and standard deviation of Y