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We are given the probability density function of a t-distribution t(µ, 1) (shown in attached image): The task is to Write down the log-likelihood function of 200 samples, derive the first and second derivative of the log likelihood function with respect to µ. I got log-likihood function for 200 sampes and the first derivative, but am having trouble figuring how to get the second derivative.

We are given the probability density function of a t-distribution t(µ, 1) (shown in attached image): The task is to Write down the log-likelihood function of 200 samples, derive the first and second derivative of the log likelihood function with respect to µ. I got log-likihood function for 200 sampes and the first derivative, but am having trouble figuring how to get the second derivative.

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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 43CR
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We are given the probability density function of a t-distribution t(µ, 1) (shown in attached image): The task is to Write down the log-likelihood function of 200 samples, derive the first and second derivative of the log likelihood function with respect to µ. I got log-likihood function for 200 sampes and the first derivative, but am having trouble figuring how to get the second derivative.

f(y): 1 T()√√ (1 + (y-μ)²)-¹.
Transcribed Image Text:f(y): 1 T()√√ (1 + (y-μ)²)-¹.
Question -200 Samples 1 deg. Freedom, unknown location Paremeter uit (1,1) a POF → f(y) = 1 T (²) √ (1 + (x-1)²) = 1 log ikinas f (Vi) (412) -√7) (1 + (Y-μ)²) = 1 (200 sommes) 1st- · 2 (M/Yi) = log f (Vi) = C-log (1 + (Vi _u)²) · 2 (MK²) (y) зм Ind. deristike 3 32" (MY) u 2.00 = log (f(x)) = log (it+ ₁ f(x)) = = = = log (f (vi)) = 200 ^ C → ²log (1 + (√²-1) ² 200 cancels since we mulive vbx -2 200 2 =X²-2²2 1 + (K-M) ² -each of the y different dotopar
Transcribed Image Text:Question -200 Samples 1 deg. Freedom, unknown location Paremeter uit (1,1) a POF → f(y) = 1 T (²) √ (1 + (x-1)²) = 1 log ikinas f (Vi) (412) -√7) (1 + (Y-μ)²) = 1 (200 sommes) 1st- · 2 (M/Yi) = log f (Vi) = C-log (1 + (Vi _u)²) · 2 (MK²) (y) зм Ind. deristike 3 32" (MY) u 2.00 = log (f(x)) = log (it+ ₁ f(x)) = = = = log (f (vi)) = 200 ^ C → ²log (1 + (√²-1) ² 200 cancels since we mulive vbx -2 200 2 =X²-2²2 1 + (K-M) ² -each of the y different dotopar
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