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Practice Exam Questions1. Find the Variance ofS2.2. LetXi, i=1,2,3, be independent Normal(i, i2) random variables. Foreach below, useXito construct a statistic with the indicated distribu-tion:(a)χ2(3)(b) t(2)(c) F(1,2)3. LetXi, i= 1, . . . , n,be independent variables from the Uniform(θ,2θ)distribution.(a) Find a function ofXthat has expected valueθ.(b) Write down the standardized version ofX, which converges in dis-tribution to a Normal(0,1).