1) Let {x,: i = 1, 2, . , n} be a set of n data points with x, > 0 for all i. Is it always true that 1 :? ΣA i=1 (ii) Is the equality in part (i) always true if x, = c for all i,where c > 0?
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- Consider two points (x0, y0) and (x1, y1). Prove that the first order Langrange polynonial is equivalent to linear interpolation.Consider a statistical decision problem (Θ, X, D, L) with Θ = {θ1, . . . , θk}. Show that if x0 = (R(θ1, δ0), . . . , R(θk, δ0)) ∈ λ(R), then δ0 is admissible. Here, R is the set of risk points, assumed to be a closed set and λ(R) denotes the set of lower boundary points of RWhich of these provides sufficient information to prove
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- find rank(AT) and nullity(A)Find S ∩ T, (S ∩ T)c, Sc ∩ Tc, S ∪ T, (S ∪ T)c, and Sc ∪ Tc (1) S = (0, 1), T = [1/2, 3/2] (2) S ={x |x2 > 4}, T = {x |x2 < 9} (3) S =(-∞, ∞), T = Ø (4) S =(-∞, -1), T = (1, ∞)they take samples of 4 fireworks for quality co from and examine them for defects. let X be the number of defective fireworks in the sample of 4.