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 the following function. f(x)equalsleft brace start 2 by 2 matrix 1st row 1st column 6 x superscript negative 7 baseline comma 2nd column x greater than 1 2nd row 1st column 0 comma 2nd column elsewhere endmatrix (a) verify that this is a valid density function. (b) evaluate f(x). (c) what is the probability that a random particle from the manufactured fuel exceeds 4 micrometers?