[All Steps] Consider a density given by f(x;θ)=0.5(1+θ x), -1≤ x≤ 1 Prove that 3X̄ is an unbiased estimator of
Question: Consider a density given by
\[f(x;\theta )=0.5(1+\theta x),\text{ }-1\le x\le 1\]Prove that \(3\bar{X}\) is an unbiased estimator of \(\theta \)
Deliverable: Word Document 
![[See Solution] Given any subset E of](/images/solutions/MC-solution-library-31145.jpg "[See Solution] Given any subset E of R and any h ∈ R, show that")
[See Solution] Given any subset E of R and any h ∈ R, show that
![[All Steps] Suppose that E is measurable](/images/solutions/MC-solution-library-31146.jpg "[All Steps] Suppose that E is measurable with m(E)=1. Show that:")
[All Steps] Suppose that E is measurable with m(E)=1. Show that:
(Solution Library) Let \mathcalE be any collection of subsets of R.
![[Steps Shown] The smallest σ -algebra containing](/images/solutions/MC-solution-library-31148.jpg "[Steps Shown] The smallest σ -algebra containing \mathcalE")
[Steps Shown] The smallest σ -algebra containing \mathcalE
![[Steps Shown] Show that \mathcalB is generated](/images/solutions/MC-solution-library-31149.jpg "[Steps Shown] Show that \mathcalB is generated by each of the following:")
[Steps Shown] Show that \mathcalB is generated by each of the following:
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