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. 2x x>1 0₁ 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 5 micrometers? f(x) = (a) The function f(x) is a valid density function because 18 (b) F(x) = { x≤ 1, x>1. for all (c) P(X> 5) = (Type an integer or decimal rounded to four decimal places as needed.) | and because_ [ f(x) dx = √2x²³dx = Of=[ -00 1
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. 2x x>1 0₁ 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 5 micrometers? f(x) = (a) The function f(x) is a valid density function because 18 (b) F(x) = { x≤ 1, x>1. for all (c) P(X> 5) = (Type an integer or decimal rounded to four decimal places as needed.) | and because_ [ f(x) dx = √2x²³dx = Of=[ -00 1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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.
- 3
x>1
f(x) =
2x
0₁
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 5 micrometers?
(a) The function f(x) is a valid density function because
(b) F(x)=
x≤ 1,
x>1.
▼for all
(c) P(X> 5) =
(Type an integer or decimal rounded to four decimal places as needed.)
O
and because
S f(x) dx =
- 00
· √2x-³3d
2x ¯³ dx = (i =
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