The particle size distribution is an important factor in solid missile.In production, there are some significant problems when the particle sizes are too large. According to past studies, it has been determined that the particle size (in micrometers) distribution is characterized by the following function. 2x3. x>1 f(x) = { 0, 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 7 micrometers? (a) The function f(x) is a valid density function because V for all V and because f(x) dx = - 3dx = (D -0 -0- O xs1, (b) F(x) = O x>1. (c) P(X > 7) =O (Type an integer or decimal rounded to four decimal places as needed.)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
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The particle size distribution is an important factor in solid missile.In production, there are some significant problems when the particle sizes are too large. According to past studies, it has been determined that the particle size (in micrometers)
distribution is characterized by the following function.
-3 х>1
2x °,
f(x) =
0,
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 7 micrometers?
V and because
- 3 dx= (D -D-
(a) The function f(x) is a valid density function because
V for all
f(x) dx =
xS1,
(b) F(x) =
х>1.
(c) P(X> 7) =O
(Type an integer or decimal rounded to four decimal places as needed.)
Transcribed Image Text:The particle size distribution is an important factor in solid missile.In production, there are some significant problems when the particle sizes are too large. According to past studies, it has been determined that the particle size (in micrometers) distribution is characterized by the following function. -3 х>1 2x °, f(x) = 0, 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 7 micrometers? V and because - 3 dx= (D -D- (a) The function f(x) is a valid density function because V for all f(x) dx = xS1, (b) F(x) = х>1. (c) P(X> 7) =O (Type an integer or decimal rounded to four decimal places as needed.)
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