Question: Let X ₁ ,…..Sn be a random sample from EXP (theta) and define \({{\bar{\theta }}_{1}}\) = \(\bar{X}\) and \({{\bar{\theta }}_{2}}\) =. \(n\bar{X}/\left( n+1 \right)\)

1. Find the variances of \({{\bar{\theta }}_{1}}\) and \({{\bar{\theta }}_{2}}\).
2. Find the MSEs of \({{\bar{\theta }}_{1}}\) and \({{\bar{\theta }}_{2}}\).
3. Compare the variances of \({{\bar{\theta }}_{1}}\) and \({{\bar{\theta }}_{2}}\). for n = 2.
4. Compare the MSEs of \({{\bar{\theta }}_{1}}\) and \({{\bar{\theta }}_{2}}\).for n = 2.
   
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