(b) Assume that Y₁, Y₂, ..., Yn are independent normal random variables with mean μ = B₁ + B₁x₂ and variance o². The probability density function of Y; is given by 1 {vi-(BO+B₁²₁)}² 9(Yi; Bo, B₁, 0²) = 20² V2πσ2 Prove that the values of the maximum likelihood estimates are Bo=y-B₁, Sty B₁ Σ₁₁ (xi — T) (Yi — Y) Σ=1(vi - π)2 STT and ¹ Σ(Yi - (Bo + B₁x₂)². n i=1 = =

MATLAB: An Introduction with Applications
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(b) Assume that Y₁, Y2, ..., Yn are independent normal random variables with mean
μ = Bo + ₁x₂ and variance o2. The probability density function of Y, is given by
1
9(Yi; Bo, B₁,0²)
{yi-(³0+3₁x₁)}²
202
=
12πσ2
Prove that the values of the maximum likelihood estimates are
Bo=y-B₁,
Σ₁ (xi-T) (Yi - y)
Σi-1
Sty
B₁
Σ=1(x; - π)2
STE
and
n
Σ(Yi − (Âo + Â₁x;)².
n
i=1
=
=
=
Transcribed Image Text:(b) Assume that Y₁, Y2, ..., Yn are independent normal random variables with mean μ = Bo + ₁x₂ and variance o2. The probability density function of Y, is given by 1 9(Yi; Bo, B₁,0²) {yi-(³0+3₁x₁)}² 202 = 12πσ2 Prove that the values of the maximum likelihood estimates are Bo=y-B₁, Σ₁ (xi-T) (Yi - y) Σi-1 Sty B₁ Σ=1(x; - π)2 STE and n Σ(Yi − (Âo + Â₁x;)². n i=1 = = =
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