T characterized by the following function. f(x)= 7x8, x>1 elsewhere (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 2 micrometers? 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 00 80 (a) The function f(x) is a valid density function because for all and because S f(x) dx = 7x- dx = = -0 8 (b) F(x)= x1, x>1. (c) P(X>2)= (Type an integer or decimal rounded to four decimal places as needed.)