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  • Mathlib/Probability/Distributions/Gaussian

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Mathlib/Probability/Distributions/Gaussian/Real.lean

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@@ -372,13 +372,13 @@ lemma gaussianReal_sub_const (hX : HasLaw X (gaussianReal μ v) P) (y : ℝ) :
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/-- If `X` is a real random variable with Gaussian law with mean `μ` and variance `v`, then `c * X`
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has Gaussian law with mean `c * μ` and variance `c ^ 2 * v`. -/
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lemma gaussianReal_const_mul (hX : HasLaw X (gaussianReal μ v) P) (c : ℝ) :
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HasLaw (fun ω ↦ c * X ω) (gaussianReal (c * μ) (c ^ 2, sq_nonneg _ * v)) P :=
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HasLaw (fun ω ↦ c * X ω) (gaussianReal (c * μ) (.mk (c ^ 2) (sq_nonneg _) * v)) P :=
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HasLaw.comp ⟨by fun_prop, gaussianReal_map_const_mul c⟩ hX
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/-- If `X` is a real random variable with Gaussian law with mean `μ` and variance `v`, then `X * c`
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has Gaussian law with mean `c * μ` and variance `c ^ 2 * v`. -/
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lemma gaussianReal_mul_const (hX : HasLaw X (gaussianReal μ v) P) (c : ℝ) :
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HasLaw (fun ω ↦ X ω * c) (gaussianReal (c * μ) (c ^ 2, sq_nonneg _ * v)) P :=
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HasLaw (fun ω ↦ X ω * c) (gaussianReal (c * μ) (.mk (c ^ 2) (sq_nonneg _) * v)) P :=
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HasLaw.comp ⟨by fun_prop, gaussianReal_map_mul_const c⟩ hX
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lemma gaussianReal_neg (hX : HasLaw X (gaussianReal μ v) P) :
@@ -389,7 +389,7 @@ lemma gaussianReal_neg (hX : HasLaw X (gaussianReal μ v) P) :
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/-- If `X` is a real random variable with Gaussian law with mean `μ` and variance `v`, then `X * c`
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has Gaussian law with mean `c * μ` and variance `c ^ 2 * v`. -/
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lemma gaussianReal_div_const (hX : HasLaw X (gaussianReal μ v) P) (c : ℝ) :
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HasLaw (fun ω ↦ X ω / c) (gaussianReal (μ / c) (v / c ^ 2, sq_nonneg _)) P :=
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HasLaw (fun ω ↦ X ω / c) (gaussianReal (μ / c) (v / .mk (c ^ 2) (sq_nonneg _))) P :=
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HasLaw.comp ⟨by fun_prop, gaussianReal_map_div_const c⟩ hX
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/-- If `X` is a real random variable with Gaussian law with mean `μ` and variance `v`, then `y - X`

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