Let X have a Weibull distribution with the pdf below. α f(x; a, B) = Ba Verify that μ = Br 1+ ¹e-(x/a)ª x20 x<0 a (1+¹). [Hint: In the integral for E(X), make the change of variable y = ( = (*) ª so that x = By¹/a.]
Let X have a Weibull distribution with the pdf below. α f(x; a, B) = Ba Verify that μ = Br 1+ ¹e-(x/a)ª x20 x<0 a (1+¹). [Hint: In the integral for E(X), make the change of variable y = ( = (*) ª so that x = By¹/a.]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let X have a Weibull distribution with the pdf below.
f(x; α, ß) =
μ =
α
X.
Using the substitution, y =
ta
Ва
0 Ba
-1e-(x/B) a
1
Verify that μ = Br| 1 + − [Hint: In the integral for E(X), make the change of variable y =
= (3)“,
α
0
- (²) ª = ²².
Ba
Now we can simplify μ as follows.
- 6°x
= ["( (₂B²) ( ² ) )e-v dy
- (B
1
= Br(1 + ²¹² )
α
α 1e-(x/B) dx
x ≥ 0
x < 0
Thus, dy =
)*ylsery dy
ва
α
= By ¹/α.]
so that x =
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dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddd96ab9-54be-46e6-927a-d9e159267b74%2F36ac960c-65f1-4c6d-a7ac-335990d72595%2Fsdgfpt_processed.png&w=3840&q=75)
Transcribed Image Text:Let X have a Weibull distribution with the pdf below.
f(x; α, ß) =
μ =
α
X.
Using the substitution, y =
ta
Ва
0 Ba
-1e-(x/B) a
1
Verify that μ = Br| 1 + − [Hint: In the integral for E(X), make the change of variable y =
= (3)“,
α
0
- (²) ª = ²².
Ba
Now we can simplify μ as follows.
- 6°x
= ["( (₂B²) ( ² ) )e-v dy
- (B
1
= Br(1 + ²¹² )
α
α 1e-(x/B) dx
x ≥ 0
x < 0
Thus, dy =
)*ylsery dy
ва
α
= By ¹/α.]
so that x =
Your answer includes 2 characters that can't be graded.
Delete your recent changes and use the pad tools to finish your answer. More information
dx.
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