How to draw "cut" areas in a contour plot

I use these commands

Show[ContourPlot[ PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x, y}],
{x, -2, 2}, {y, -2, 2}, Contours -> {0.05, 0.09}, ContourShading -> {None, Green},
ContourStyle -> {{Thickness[0.004], Opacity[1]}, {Thickness[0.004], Opacity[1]}}],
ContourPlot[PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x, y}],
{x, -2, 2}, {y, -2, 2}, Contours -> {0.06, 0.07}, ContourShading -> {None, Yellow},
ContourStyle -> {{Thickness[0.005], Dashed,
Opacity[1]}, {Thickness[0.005], Dashed, Opacity[1]}}]]


to plot the figure on the left

I want to "cut" the area corresponding to $\mathbb{R}^2-\{x\geq 0 \&\& y\geq 0\}$ to obtain something like the figure on the right, i.e. covering the cutted area with a texture made of diagonal lines.

How can I do? I tried with "Mesh" but the lines appear in all the Frame and not only in the interested areas.

dist = MultinormalDistribution[
{0, 0}, {{2, 1/2}, {1/2, 1}}];

rgn = ImplicitRegion[{0.05 <= PDF[dist, {x, y}] <= 0.09,
-2 <= x <= 2, -2 <= y <= 2, ! (x >= 0 && y >= 0)}, {x, y}];

Show[
ContourPlot[
PDF[dist, {x, y}], {x, -2, 2}, {y, -2, 2},
Contours -> {0.05, 0.09},
ContourStyle -> Thickness[0.004]],
ContourPlot[
PDF[dist, {x, y}], {x, -2, 2}, {y, -2, 2},
Contours -> {0.06, 0.07},
ContourStyle ->
Directive[Thickness[0.005], Dashed]],
ContourPlot[(x + y) Boole[! (x >= 0 && y >= 0)],
{x, -2, 2}, {y, -2, 2},
Contours -> 50,
RegionFunction -> ({#1, #2} ∈ rgn &)]]


EDIT: A variation using RegionPlot

{outerRgn, innerRgn, rgn} =
ImplicitRegion[
{#[[1]] <= PDF[dist, {x, y}] <= #[[2]],
-2 <= x <= 2, -2 <= y <= 2, #[[3]]}, {x, y}] & /@
{{0.05, 0.09,
True}, {0.06, 0.07, True}, {0.05, 0.09, ! (x >= 0 && y >= 0)}};

Show[
RegionPlot[{outerRgn, innerRgn},
PlotRange -> {{-2, 2}, {-2, 2}},
PlotStyle -> {Green, Yellow}],
ContourPlot[(x + y) Boole[! (x >= 0 && y >= 0)],
{x, -2, 2}, {y, -2, 2},
Contours -> 50,
RegionFunction -> ({#1, #2} \[Element] rgn &),
BoundaryStyle -> Thick]]


Add a RegionFunction:

Show[
ContourPlot[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}], {x, -2, 2}, {y, -2, 2}, Contours -> {0.05, 0.09},
ContourStyle -> {{Thickness[0.004], Opacity[1]}, {Thickness[0.004],
Opacity[1]}},
RegionFunction -> Function[{x, y, z}, x >= 0 && y >= 0]],
ContourPlot[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}], {x, -2, 2}, {y, -2, 2}, Contours -> {0.06, 0.07},
ContourStyle -> {{Thickness[0.005], Dashed,
Opacity[1]}, {Thickness[0.005], Dashed, Opacity[1]}},
RegionFunction -> Function[{x, y, z}, x >= 0 && y >= 0]]]


• Thank you, but this is not exactly what I want. I would like to show the cutted are but with a texture made of diagonal lines, as shown in the figure on the right Commented Aug 31, 2016 at 19:52

If I understand which region you are interested in correctly:

Show[ContourPlot[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}], {x, -2, 2}, {y, -2, 2}, Contours -> {0.05, 0.09},
ContourStyle -> {{Thickness[0.004], Opacity[1]}, {Thickness[0.004],
Opacity[1]}},
RegionFunction -> Function[{x, y, z}, x <= 0 || y <= 0]],
ContourPlot[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}], {x, -2, 2}, {y, -2, 2}, Contours -> {0.06, 0.07},
ContourStyle -> {{Thickness[0.005], Dashed,
Opacity[1]}, {Thickness[0.005], Dashed, Opacity[1]}},
RegionFunction -> Function[{x, y, z}, x <= 0 || y <= 0]]]


yielding:

Edit:

This may not be the most elegant solution, but:

Show[ContourPlot[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}], {x, -2, 2}, {y, -2, 2}, Contours -> {0.05, 0.09},
ContourStyle -> {{Thickness[0.004], Opacity[1]}, {Thickness[0.004],
Opacity[1]}}],
ContourPlot[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}], {x, -2, 2}, {y, -2, 2}, Contours -> {0.06, 0.07},
ContourStyle -> {{Thickness[0.005], Dashed,
Opacity[1]}, {Thickness[0.005], Dashed, Opacity[1]}}],
ListLinePlot[{{0,
FindRoot[
Evaluate[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}] /. x -> 0] == .05, {y, 1}][[1, 2]]}, {0,
FindRoot[
Evaluate[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}] /. x -> 0] == .09, {y, 1}][[1, 2]]}},
PlotStyle -> Directive[Black, AbsoluteThickness[2]]],
ListLinePlot[{{FindRoot[
Evaluate[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}] /. y -> 0] == .09, {x, 1}][[1, 2]],
0}, {FindRoot[
Evaluate[
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}] /. y -> 0] == .05, {x, 1}][[1, 2]], 0}},
PlotStyle -> Directive[Black, AbsoluteThickness[2]]],
ContourPlot[Sin[x*10 + y*10] == 0, {x, -2, 2}, {y, -2, 2},
ContourStyle -> Directive[Black, AbsoluteThickness[2]],
RegionFunction ->
Function[{x, y,
z}, .05 <=
PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x,
y}] <= .09 && (x <= 0 || y <= 0)]]]


gives:

• Thank you, but this is not exactly what I want. I would like to show the cutted are but with a texture made of diagonal lines, as shown in the figure on the right Commented Aug 31, 2016 at 19:52

This can all be done with a single call to ContourPlot[] and the clever use of MeshFunctions:

mnpdf[x_, y_] = PDF[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], {x, y}];

ContourPlot[mnpdf[x, y], {x, -2, 2}, {y, -2, 2}, Contours -> {0.05, 0.06, 0.07, 0.09},
ContourShading -> {None, Green, Yellow, Green},
ContourStyle -> {Directive[Thickness[0.002], Opacity[1]],
Directive[Thickness[0.005], Dashed, Opacity[1]],
Directive[Thickness[0.005], Dashed, Opacity[1]]}, Mesh -> 25,
MeshFunctions -> {(#1 + #2) Boole[! (#1 > 0 && #2 > 0) &&
0.05 < mnpdf[#1, #2] < 0.09] &}, MeshStyle -> Opacity[1]]