?Consider the probability density function \(f(x)=c(1+\theta x)\), \(\quad-1 \leq x \leq
Chapter 7, Problem 7.4.4(choose chapter or problem)
Consider the probability density function
\(f(x)=c(1+\theta x)\), \(\quad-1 \leq x \leq 1\)
a. Find the value of the constant c.
b. What is the moment estimator for \(\theta\)?
c. Show that \(\hat{\theta}=3 \bar{X}\) is an unbiased estimator for \(\theta\). d. Find the maximum likelihood estimator for \(\theta\).
Text Transcription:
f(x)=c(1+\theta x)
\quad-1 \leq x \leq 1
\hat{\theta}=3 \bar{X}
\theta
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