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{:[=int_(0)^(theta)ze^(-z)dz],[=sqrt2=1.],[E(y)=1+theta". "],[mu_(1)=1+theta]:}Replace u_(1) by bar(y) to get moments estionatorbar(y)-1= hat(theta)hat(theta)_(1) is unbiasid estimator of theta.{:[E( bar(y)-1)=E( bar(y))-1],[=1+theta-1=theta]:}{:[V(y-theta)=E(y-theta)^(2)-E^(2)(y-theta)],[=>v(y)=E(y-theta)^(2)-E^(2)(y-theta)],[E(y-theta)^(2)=int_(theta)^(oo)(y-theta)^(2)e^(-(y-theta))dy],[=int_(0)^(oo)z^(22)e^(-z)dz∣{:[y-theta=z],[dy=dz]:}],[=sqrt3=2],[V(y)=2-1=1],[v( hat(O)_(1))=v( bar(y)-1)=v( bar(y))=(v(Y_(i)))/(n)],[=(1)/(n)". "],[=e^(-sum_(i=1)^(n)(y_(i)-theta))I(theta < y_((1)) < cdots < y_((n)))]:}we need to minimise sum_(i=1)(y_(i)-theta)So the ... See the full answer