C₁=-47³1-37²² +127²7²-67¹. Problem 3.44. Consider the probability density given by (2a)-¹ for x≤ a for r>a p(x) = (3.100) (a) Sketch the dependence of p(x) on z. (b) Find the first four moments of p(x). (c) Calculate the value of the fourth-order cumulant C₁ defined in (3.99)). What is C₁ for the probability density in (3.100)? (3.99) 10

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Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
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Statistical Physics P3.44 Please supply all necessary solutions, thank you!
C₁=¹-47³-37²² +127²7²-67¹.
Problem 3.44. Consider the probability density given by
(2a)-¹ for x≤ a
10 for r > a
(3.99)
p(x) =
(3.100)
(a) Sketch the dependence of p(x) on x. (b) Find the first four moments of p(x). (c) Calculate the
value of the fourth-order cumulant C₁ defined in (3.99)). What is C4 for the probability density
in (3.100)?
Transcribed Image Text:C₁=¹-47³-37²² +127²7²-67¹. Problem 3.44. Consider the probability density given by (2a)-¹ for x≤ a 10 for r > a (3.99) p(x) = (3.100) (a) Sketch the dependence of p(x) on x. (b) Find the first four moments of p(x). (c) Calculate the value of the fourth-order cumulant C₁ defined in (3.99)). What is C4 for the probability density in (3.100)?
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