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94 lines
2.9 KiB
Python
94 lines
2.9 KiB
Python
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from manimlib.imports import *
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from active_projects.eop.reusable_imports import *
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class IllustrateAreaModelExpectation(Scene):
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def construct(self):
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formula = TexMobject("E[X] = \sum_{i=1}^N p_i x_i").move_to(3 * LEFT + UP)
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self.play(Write(formula))
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x_scale = 5.0
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y_scale = 1.0
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probabilities = np.array([1./8, 3./8, 3./8, 1./8])
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prob_strings = ["{1\over 8}","{3\over 8}","{3\over 8}","{1\over 8}"]
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cumulative_probabilities = np.cumsum(probabilities)
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cumulative_probabilities = np.insert(cumulative_probabilities, 0, 0)
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y_values = np.array([0, 1, 2, 3])
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hist = Histogram(probabilities, y_values,
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mode = "widths",
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x_scale = x_scale,
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y_scale = y_scale,
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x_labels = "none"
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)
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flat_hist = Histogram(probabilities, 0 * y_values,
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mode = "widths",
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x_scale = x_scale,
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y_scale = y_scale,
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x_labels = "none"
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)
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self.play(FadeIn(flat_hist))
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self.play(
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ReplacementTransform(flat_hist, hist)
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)
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braces = VGroup()
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p_labels = VGroup()
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# add x labels (braces)
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for (p,string,bar) in zip(probabilities, prob_strings,hist.bars):
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brace = Brace(bar, DOWN, buff = 0.1)
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p_label = TexMobject(string).next_to(brace, DOWN, buff = SMALL_BUFF).scale(0.7)
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group = VGroup(brace, p_label)
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braces.add(brace)
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p_labels.add(p_label)
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self.play(
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LaggedStartMap(FadeIn,braces),
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LaggedStartMap(FadeIn, p_labels)
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)
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y_average = np.mean(y_values)
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averaged_y_values = y_average * np.ones(np.shape(y_values))
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averaged_hist = flat_hist = Histogram(probabilities, averaged_y_values,
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mode = "widths",
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x_scale = x_scale,
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y_scale = y_scale,
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x_labels = "none",
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y_labels = "none"
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).fade(0.2)
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ghost_hist = hist.copy().fade(0.8)
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self.bring_to_back(ghost_hist)
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self.play(Transform(hist, averaged_hist, run_time = 3))
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self.wait()
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average_brace = Brace(averaged_hist, RIGHT, buff = 0.1)
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average_label = TexMobject(str(y_average)).scale(0.7)
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average_label.next_to(average_brace, RIGHT, SMALL_BUFF)
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average_group = VGroup(average_brace, average_label)
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one_brace = Brace(averaged_hist, DOWN, buff = 0.1)
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one_p_label = TexMobject(str(1)).next_to(one_brace, DOWN, buff = SMALL_BUFF).scale(0.7)
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one_group = VGroup(one_brace, one_p_label)
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self.play(
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FadeIn(average_group),
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Transform(braces, one_brace),
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Transform(p_labels, one_p_label),
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)
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rect = SurroundingRectangle(formula, buff = 0.5 * MED_LARGE_BUFF)
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self.play(ShowCreation(rect))
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