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: Expression for density function of T, in the convolution, isn't (t-s1) term extra?

: Expression for density function of T, in the convolution, isn't (t-s1) term extra?

Calculus For The Life Sciences
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.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 23E: Find derivatives of the functions defined as follows. fz=2z+e-z22
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Step 3: Expression for density function of T, in the convolution, isn't (t-s1) term extra?

 

Substituting this into the expression for the density function of T, we get: -S₁/0 e fr(t) = = = S²: -∞ 1 e 12/27 (1-s₁ ). e 0² -∞ (t-₁)e (t-s₁)/8 (t-₁)e ・S² (t−s₁₂) · e -∞ 88 e S₁ (t-s₁) e e -S1₁-t+S₁ 0 = 1/2 f(t-s₂). eds₁ 0² -ds₁ ds₁ 1 ds₁
Transcribed Image Text:Substituting this into the expression for the density function of T, we get: -S₁/0 e fr(t) = = = S²: -∞ 1 e 12/27 (1-s₁ ). e 0² -∞ (t-₁)e (t-s₁)/8 (t-₁)e ・S² (t−s₁₂) · e -∞ 88 e S₁ (t-s₁) e e -S1₁-t+S₁ 0 = 1/2 f(t-s₂). eds₁ 0² -ds₁ ds₁ 1 ds₁
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