Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>=...

Let x,y ∈ R3 such that x = (x₁,x₂,x₃) and y = (y₁,y_2,y₃) determine if <x,y>= x1y1+2x₂y₂+3x₃y₃

is an inner product

Expert Solution

Colby Messinger answered 1 year ago

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf...

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf of Y1, Y2, Y3, and the marginal pdfs.

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2...

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2 = X1 −X2, Y3 =X1 −X3. Find the joint pdf of Y = (Y1,Y2,Y3)′ using : Multivariate normal distribution properties.

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t...

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Observation x1 y1 x2 y2 x3 y3 x4 y4 1 10 8.04 10 9.14 10 7.46...

Observation x1 y1 x2 y2 x3 y3 x4 y4 1 10 8.04 10 9.14 10 7.46 8 6.58 2 8 6.95 8 8.14 8 6.77 8 5.76 3 13 7.58 13 8.74 13 12.74 8 7.71 4 9 8.81 9 8.77 9 7.11 8 8.84 5 11 8.33 11 9.26 11 7.81 8 8.47 6 14 9.96 14 8.1 14 8.84 8 7.04 7 6 7.24 6 6.13 6 6.08 8 5.25 8 4 4.26 4 3.1 4 5.39 19...

Anscombe's Data Observation x1 y1 x2 y2 x3 y3 x4 y4 1 10 8.04 10 9.14...

Anscombe's Data Observation x1 y1 x2 y2 x3 y3 x4 y4 1 10 8.04 10 9.14 10 7.46 8 6.58 2 8 6.95 8 8.14 8 6.77 8 5.76 3 13 7.58 13 8.74 13 12.74 8 7.71 4 9 8.81 9 8.77 9 7.11 8 8.84 5 11 8.33 11 9.26 11 7.81 8 8.47 6 14 9.96 14 8.1 14 8.84 8 7.04 7 6 7.24 6 6.13 6 6.08 8 5.25 8 4 4.26 4 3.1 4...

1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1 −x2|+|y1 −y2|. (a) Prove...

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Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of a...

Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of a random sample of size 5 from a continuous distribution with median m. What is P(Y2 < m < Y4)?

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Consider a random sample (X1, Y1), (X2, Y2), . . . , (Xn, Yn) where Y | X = x is modeled by Y=β0+β1x+ε, ε∼N(0,σ^2), where β0,β1and σ^2 are unknown. Let β1 denote the mle of β1. Derive V(βhat1).

Loading Pandas DataFrames and Creating Multiple Plots and Subplots x1 y1 y1_pred x2 y2 y2_pred x3...

Loading Pandas DataFrames and Creating Multiple Plots and Subplots x1 y1 y1_pred x2 y2 y2_pred x3 y3 y3_pred x4 y4 y4_pred 0 10 8.04 8.001000 10 9.14 8.000909 10 7.46 7.999727 8 6.58 7.001 1 8 6.95 7.000818 8 8.14 7.000909 8 6.77 7.000273 8 5.76 7.001 2 13 7.58 9.501273 13 8.74 9.500909 13 12.74 9.498909 8 7.71 7.001 3 9 8.81 7.500909 9 8.77 7.500909 9 7.11 7.500000 8 8.84 7.001 4 11 8.33 8.501091 11 9.26 8.500909...

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z....

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z. Show that the relation∼is an equivalence relation and describe the equivalence class of the point (0,1).

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