Question

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) = 3x-4, x>1 10, 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 9 micrometers? (a) The function f(x) is a valid density function because f(x)21 for all XER and because fo dx= [ 3x-4dx= (-x-3) 1 * =1 10, x51, (b) F(x)= | 1-x-3), x>1. (C) P(X> 9) = 0.999 (Type an integer or decimal rounded to four decimal places as needed.)

Answer 1

a> $(2): 324 30 [* 271 a zty in the ai]. Tisce) dz = ſs«'de a spel ! - 5(e) yo and fes des i fond zelf 5 F68)= 2(852) - 1 scandy - 5 3g "dy. Spo: 1-x3 .F(7) 0 of 251 >> P(x>9) = 1 - P(<$q) = |-F() = 1-(1-93) - 98 0.00 * 0.0014) ' (1-x-3 if xyl