part 1

func/drawBackGround.m

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+
+function drawBackGround(Radius, Width, Length)
+% prepare figure
+hold on
+    % - draw circle
+d_ang = 0 : pi/100 : 2*pi;
+plot(Radius*cos(d_ang), Radius*sin(d_ang), '-');
+    % - draw rect
+line([
+    -Length/2, -Length/2, Length/2, Length/2, -Length/2
+], [
+    -Width/2, Width/2, Width/2, -Width/2, -Width/2
+]);
+
+axis equal
+end

func/getDisProb.m

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+% compute distributation
+function [score, totalTimes, prs, d_rx, d_bo] = getDisProb(R, N, Radius, Length, Width, isPlot, method)
+score = 0;
+totalTimes = 0;
+for m = 1 : R
+    for n = 1 : N
+        [x, y] = method(Radius);
+        totalTimes = totalTimes + 1;
+        if isInRect(Length/2, Width/2, x, y)
+            score = score + 1;
+            if isPlot
+                d_rx = plot(x, y, 'rx');
+            end
+        else
+            if isPlot
+                d_bo = plot(x, y, 'bo');
+            end
+        end
+    end
+    prs = score / totalTimes;
+end

func/isInRect.m

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+
+% judge if a position in a rectangle
+function res = isInRect(x, y, x_, y_)
+    if abs(x_) < x && abs(y_) < y
+        res = true;
+    else
+        res = false;
+    end
+end

func/normrnd_circle.m

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+% get random position in circle
+function [res_x, res_y] = normrnd_circle(r)
+
+    ang = 2*pi*rand(1);
+    t_r = normrnd(0, r);
+    res_x = t_r*cos(ang);
+    res_y = t_r*sin(ang);
+
+end

func/unifrnd_circle.m

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+% get random position in circle
+function [res_x, res_y] = unifrnd_circle(r)
+
+    while true
+        res_x = unifrnd(-r, r, 1, 1);
+        res_y = unifrnd(-r, r, 1, 1);
+        ans_r = sqrt(res_x^2 + res_y^2);
+        if ans_r < r
+            break
+        end
+    end
+
+end
+

t2.m

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+
+% init
+clear
+addpath(genpath('./func/'));
+
+% declear const
+Radius = sqrt(5);
+Width = 2;
+Length = 4;
+
+% params input
+N = input("Shots Times: ");
+R = input("Repeating Times: ");
+
+% draw background
+drawBackGround(Radius, Width, Length);
+
+% calculate prs
+[score, totalTimes, prs, d_rx, d_bo] = getDisProb(R, N, Radius, Length, Width, true, @unifrnd_circle);
+
+% add legend
+legend([d_rx, d_bo], {'scored shot', 'missed shot'});
+t_s = sprintf('Scatter plot for N=%d and R=%d. prs=%d%%', N, R, prs*100);
+title(t_s);
+
+display(prs);
+

t4.m

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+
+% init
+clear
+addpath(genpath('./func/'));
+
+% declear const
+Radius = sqrt(5);
+Width = 2;
+Length = 4;
+
+% declear params
+N = [100, 1000, 10000, 100000];
+R = 5;
+
+% declear var
+array_prs = [];
+
+% calculate prs
+for i = 1 : numel(N)
+    [score, totalTimes, prs] = getDisProb(R, N(i), Radius, Length, Width, false, @unifrnd_circle);
+    array_prs = [array_prs, prs];
+end
+
+disp(array_prs);
+
+plot(N, array_prs);
+xlabel('N random shots');
+ylabel('Probability');
+t_s = sprintf('Scatter plot for N with R=%d.', R);
+title(t_s);

t5.m

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+
+% init
+clear
+addpath(genpath('./func/'));
+
+% declear const
+Radius = sqrt(5);
+Width = 2;
+Length = 4;
+
+% declear params
+N = 1000;
+R = [5, 10, 15, 20];
+
+% declear var
+array_prs = [];
+
+% calculate prs
+for i = 1 : numel(R)
+    [score, totalTimes, prs] = getDisProb(R(i), N, Radius, Length, Width, false, @unifrnd_circle);
+    array_prs = [array_prs, prs];
+end
+
+disp(array_prs);
+
+plot(R, array_prs);
+xlabel('R random shots');
+ylabel('Probability');
+t_s = sprintf('Scatter plot for R with N=%d.', N);
+title(t_s);

t7_2.m

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+
+% init
+clear
+addpath(genpath('./func/'));
+
+% declear const
+Radius = sqrt(5);
+Width = 2;
+Length = 4;
+
+% params input
+N = input("Shots Times: ");
+R = input("Repeating Times: ");
+
+% draw background
+drawBackGround(Radius, Width, Length);
+
+% calculate prs
+[score, totalTimes, prs, d_rx, d_bo] = getDisProb(R, N, Radius, Length, Width, true, @normrnd_circle);
+
+% add legend
+legend([d_rx, d_bo], {'scored shot', 'missed shot'});
+t_s = sprintf('Scatter plot for N=%d and R=%d. prs=%d%%', N, R, prs*100);
+title(t_s);
+
+display(prs);
+

t7_4.m

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+
+% init
+clear
+addpath(genpath('./func/'));
+
+% declear const
+Radius = sqrt(5);
+Width = 2;
+Length = 4;
+
+% declear params
+N = [100, 1000, 10000, 100000];
+R = 5;
+
+% declear var
+array_prs = [];
+
+% calculate prs
+for i = 1 : numel(N)
+    [score, totalTimes, prs] = getDisProb(R, N(i), Radius, Length, Width, false, @normrnd_circle);
+    array_prs = [array_prs, prs];
+end
+
+disp(array_prs);
+
+plot(N, array_prs);
+xlabel('N random shots');
+ylabel('Probability');
+t_s = sprintf('Scatter plot for N with R=%d.', R);
+title(t_s);

t7_5.m

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+
+% init
+clear
+addpath(genpath('./func/'));
+
+% declear const
+Radius = sqrt(5);
+Width = 2;
+Length = 4;
+
+% declear params
+N = 1000;
+R = [5, 10, 15, 20];
+
+% declear var
+array_prs = [];
+
+% calculate prs
+for i = 1 : numel(R)
+    [score, totalTimes, prs] = getDisProb(R(i), N, Radius, Length, Width, false, @normrnd_circle);
+    array_prs = [array_prs, prs];
+end
+
+disp(array_prs);
+
+plot(R, array_prs);
+xlabel('R random shots');
+ylabel('Probability');
+t_s = sprintf('Scatter plot for R with N=%d.', N);
+title(t_s);