Let α' > 0, α2 > 0, with a, +":-a.Then a. Use this equation to derive...
Let 0 < γ < α . Then a 100(1 − α )% CI for μ when n is large is Xbar+/-zγ*(s/sqrt(n))The choice γ = α /2 yields the usual interval derived in Section 8.2; if γ ≠ α /2, this confidence interval is not symmetric about . The width of the interval is W=s(zγ+ zα-γ)/sqrt(n). Show that w is minimized for the choice γ = α /2, so that the symmetric interval is the shortest. [ Hints : (a)...
(Bernoulli Equations) Let p, f : I → R be continous functions defined on an interval I of R. Then for every α є R\ {0, 1), the 1st-order differential equation is called Bernoulli equation. It is a nonlinear ordinary differential equation. (a) Use the literature and describe in brief steps a method to find a solution of equation (1) Hint: See Trench, p.63 (b) Find all solutions to the following two differential equations. Use Mathematica to plot a direction...
In the simple linear regression with zero-constant item for (xi , yi) where i = 1, 2, · · · , n, Yi = βxi + i where {i} n i=1 are i.i.d. N(0, σ2 ). (a) Derive the normal equation that the LS estimator, βˆ, satisfies. (b) Show that the LS estimator of β is given by βˆ = Pn i=1 P xiYi n i=1 x 2 i . (c) Show that E(βˆ) = β, V ar(βˆ) = σ...