<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/022583c3-7af7-4c2f-b11f-dc1f0fbd5484/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1b ws10"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1b ws10">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls1b ws10"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls1b ws10">Estatística Aplicada - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls1b ws10"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls1b ws10">DISTRIBUIÇÃO DO QUOCIENTE DE </div><div class="t m0 x1 h5 y8 ff3 fs2 fc0 sc0 ls1b ws10">VARIÂNCIAS E DA DIFERENÇA DE </div><div class="t m0 x1 h5 y9 ff3 fs2 fc0 sc0 ls1b ws10">PROPORÇÕES </div><div class="t m0 x1 h6 ya ff2 fs3 fc1 sc0 ls1b ws10"> </div><div class="t m0 x1 h7 yb ff3 fs4 fc1 sc0 ls1b ws10">Distribuição do quociente de variâncias </div><div class="t m0 x1 h8 yc ff2 fs3 fc0 sc0 ls1b ws10">Seja <span class="_0 blank"> </span><span class="ff4">\ue73a</span></div><div class="t m0 x3 h9 yd ff4 fs5 fc0 sc0 ls0">\ueb35<span class="fs3 ls1b ws0 v1">, \u2026 , \ue73a</span></div><div class="t m0 x4 ha yd ff4 fs5 fc0 sc0 ls1">\uebe1<span class="ff2 fs3 ls1b ws10 v1"> <span class="_0 blank"> </span>a.a <span class="_0 blank"> </span>de <span class="_0 blank"> </span><span class="ff4 ws1">\ue73a<span class="_1 blank"> </span>\u223c<span class="_2 blank"> </span>\ue730 <span class="ws2 v2">(</span><span class="ls2">\ue7e4</span></span></span><span class="ls3">\uebd1<span class="fs3 ls1b ws10 v1"> \ue7ea</span></span></div><div class="t m0 x5 hb ye ff4 fs5 fc0 sc0 ls1b">\uebd1</div><div class="t m0 x6 hc yf ff4 fs5 fc0 sc0 ls4">\ueb36<span class="fs3 ls1b ws2 v3">)<span class="ff2 ws10 v4">. <span class="_0 blank"> </span>Seja <span class="_0 blank"> </span><span class="ff4">\ue73b</span></span></span></div><div class="t m0 x7 h9 yd ff4 fs5 fc0 sc0 ls0">\ueb35<span class="fs3 ls1b ws0 v1">, \u2026 , \ue73b</span></div><div class="t m0 x8 h9 yd ff4 fs5 fc0 sc0 ls5">\uebe0<span class="ff2 fs3 ls1b ws10 v1"> <span class="_0 blank"> </span>a.a <span class="_0 blank"> </span>de <span class="_0 blank"> </span><span class="ff4 ws3">\ue73b<span class="_1 blank"> </span>\u223c<span class="_2 blank"> </span>\ue730(\ue7e4 </span></span><span class="ls6">\uebd2<span class="fs3 ls1b ws0 v1">, \ue7ea</span></span></div><div class="t m0 x9 hb ye ff4 fs5 fc0 sc0 ls1b">\uebd2</div><div class="t m0 xa hd yf ff4 fs5 fc0 sc0 ls4">\ueb36<span class="fs3 ls1b ws2 v5">)<span class="ff2 ws10">. <span class="_0 blank"> </span>Considere <span class="_0 blank"> </span><span class="ff4 ls7">\ue73a</span> </span></span></div><div class="t m0 x1 h8 y10 ff2 fs3 fc0 sc0 ls8 ws10">e <span class="ff4 ls9">\ue73b</span><span class="ls1b"> v.a\u2019s independentes. </span></div><div class="t m0 x1 h6 y11 ff2 fs3 fc0 sc0 ls1b ws10">Então: </div><div class="t m0 xb he y12 ff4 fs3 fc0 sc0 ls1b ws4">\ue728<span class="_1 blank"> </span>= <span class="v6">\ue7ea</span></div><div class="t m0 xc hb y13 ff4 fs5 fc0 sc0 ls1b">\uebd2</div><div class="t m0 xd hd y14 ff4 fs5 fc0 sc0 ls4">\ueb36<span class="fs3 ls1b ws10 v5"> \ue735</span></div><div class="t m0 xe hb y13 ff4 fs5 fc0 sc0 ls1b">\uebd1</div><div class="t m0 xf hb y14 ff4 fs5 fc0 sc0 ls1b">\ueb36</div><div class="t m0 x10 h8 y15 ff4 fs3 fc0 sc0 ls1b">\ue7ea</div><div class="t m0 xc hb y16 ff4 fs5 fc0 sc0 ls1b">\uebd1</div><div class="t m0 xd hd y17 ff4 fs5 fc0 sc0 ls4">\ueb36<span class="fs3 ls1b ws10 v5"> \ue735</span></div><div class="t m0 xe hb y16 ff4 fs5 fc0 sc0 ls1b">\uebd2</div><div class="t m0 xf hf y17 ff4 fs5 fc0 sc0 lsa">\ueb36<span class="fs3 ls1b ws4 v7">\u223c \ue728</span></div><div class="t m0 x11 hb y18 ff4 fs5 fc0 sc0 ls1b ws10">\uebe1\ueb3f\ueb35, \uebe0\ueb3f\ueb35<span class="_3 blank"> </span><span class="ff2 fs3 v1"> </span></div><div class="t m0 x1 h7 y19 ff3 fs4 fc1 sc0 ls1b ws10"> </div><div class="t m0 x1 h7 y1a ff3 fs4 fc1 sc0 ls1b ws10">Distribuição da diferença entre duas proporções amostrais<span class="_0 blank"> </span> </div><div class="t m0 x1 h8 y1b ff2 fs3 fc0 sc0 ls1b ws10">Sejam <span class="_4 blank"> </span><span class="ff4 ls7">\ue73a</span> <span class="_4 blank"> </span>e <span class="_4 blank"> </span><span class="ff4 ls9">\ue73b</span> <span class="_4 blank"> </span>v.a\u2019s <span class="_4 blank"> </span>independentes <span class="_4 blank"> </span>com <span class="_4 blank"> </span>distrib<span class="_5 blank"></span>uição <span class="_4 blank"> </span>Bernoulli <span class="_4 blank"> </span>de <span class="_4 blank"> </span>parâmetros <span class="_4 blank"> </span><span class="ff4">\ue74c</span></div><div class="t m0 x12 h9 y1c ff4 fs5 fc0 sc0 ls3">\uebd1<span class="ff2 fs3 ls1b ws10 v1"> <span class="_4 blank"> </span>e <span class="_4 blank"> </span><span class="ff4">\ue74c</span></span></div><div class="t m0 x13 hb y1c ff4 fs5 fc0 sc0 lsb">\uebd2<span class="ff2 fs3 ls1b ws10 v1">, </span></div><div class="t m0 x1 h8 y1d ff2 fs3 fc0 sc0 ls1b ws10">respectivamente. Sejam <span class="ff4">\ue73a</span></div><div class="t m0 x14 h9 y1e ff4 fs5 fc0 sc0 ls0">\ueb35<span class="fs3 ls1b ws5 v1">, \u2026 , \ue73a</span></div><div class="t m0 x15 h9 y1e ff4 fs5 fc0 sc0 ls1">\uebe1<span class="ff2 fs3 ls1b ws10 v1"> a.a de <span class="ff4 ls7">\ue73a</span> e <span class="ff4">\ue73b</span></span></div><div class="t m0 x16 h9 y1e ff4 fs5 fc0 sc0 ls4">\ueb35<span class="fs3 ls1b ws10 v1">,<span class="_6 blank"> </span>\u2026<span class="_6 blank"> </span>,<span class="_6 blank"> </span> \ue73b</span></div><div class="t m0 x17 h9 y1e ff4 fs5 fc0 sc0 lsc">\uebe0<span class="ff2 fs3 ls1b ws10 v1"> a.a de <span class="ff4 ls9">\ue73b</span> e considere: </span></div><div class="t m0 x18 h8 y1f ff4 fs3 fc0 sc0 ls1b">\ue732</div><div class="t m0 x19 h8 y20 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x1a h10 y21 ff4 fs5 fc0 sc0 lsd">\uebd1<span class="fs3 lse v1">=<span class="ls1b v6">1</span></span></div><div class="t m0 x6 h11 y22 ff4 fs3 fc0 sc0 lsf">\ue74a<span class="ls1b ws6 v8">\uedcd \ue73a</span></div><div class="t m0 xe hb y21 ff4 fs5 fc0 sc0 ls1b">\uebdc</div><div class="t m0 x1b hb y23 ff4 fs5 fc0 sc0 ls1b">\uebe1</div><div class="t m0 x1c h12 y24 ff4 fs5 fc0 sc0 ls1b ws7">\uebdc \ueb40\ueb35<span class="_7 blank"> </span><span class="fs3 ws10 v9"> <span class="ff2">e </span>\ue732</span></div><div class="t m0 x1d h8 y20 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x16 h10 y21 ff4 fs5 fc0 sc0 ls10">\uebd2<span class="fs3 ls11 v1">=<span class="ls1b v6">1</span></span></div><div class="t m0 x1e h11 y22 ff4 fs3 fc0 sc0 ls12">\ue749<span class="ls1b ws6 v8">\uedcd \ue73b</span></div><div class="t m0 x1f hb y21 ff4 fs5 fc0 sc0 ls1b">\uebdc</div><div class="t m0 x20 hb y23 ff4 fs5 fc0 sc0 ls1b">\uebe0</div><div class="t m0 x17 hb y24 ff4 fs5 fc0 sc0 ls1b ws7">\uebdc \ueb40\ueb35</div><div class="t m0 x21 h6 y1f ff2 fs3 fc0 sc0 ls1b ws10"> </div><div class="t m0 x1 h6 y25 ff2 fs3 fc0 sc0 ls1b ws10">Então </div><div class="t m0 x22 h8 y26 ff4 fs3 fc0 sc0 ls1b ws8">\ue727 \ued63\ue732</div><div class="t m0 x23 h8 y27 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x24 h9 y28 ff4 fs5 fc0 sc0 ls13">\uebd1<span class="fs3 ls1b ws9 v1">\u2212 \ue732</span></div><div class="t m0 x25 h8 y27 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x26 h9 y28 ff4 fs5 fc0 sc0 ls6">\uebd2<span class="fs3 ls1b ws8 v1">\ued67<span class="_2 blank"> </span>=<span class="_2 blank"> </span>\ue727 \ued63\ue732</span></div><div class="t m0 x27 h8 y27 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 xf h9 y28 ff4 fs5 fc0 sc0 ls14">\uebd1<span class="fs3 ls1b ws8 v1">\ued67<span class="_8 blank"> </span>\u2212<span class="_8 blank"> </span>\ue727 \ued63\ue732</span></div><div class="t m0 x8 h8 y27 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x28 h9 y28 ff4 fs5 fc0 sc0 ls6">\uebd2<span class="fs3 ls1b wsa v1">\ued67 = \ue74c</span></div><div class="t m0 x29 h9 y28 ff4 fs5 fc0 sc0 ls13">\uebd1<span class="fs3 ls1b ws9 v1">\u2212 \ue74c</span></div><div class="t m0 x2a hb y28 ff4 fs5 fc0 sc0 lsb">\uebd2<span class="ff2 fs3 ls1b ws10 v1"> </span></div><div class="t m0 x2b h8 y29 ff4 fs3 fc0 sc0 ls1b wsb">\ue738\ue73d\ue74e \ued6b\ue732</div><div class="t m0 x2c h8 y2a ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x2d h9 y2b ff4 fs5 fc0 sc0 ls15">\uebd1<span class="fs3 ls1b ws9 v1">\u2212 \ue732</span></div><div class="t m0 x2e h8 y2a ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x2f h9 y2b ff4 fs5 fc0 sc0 ls6">\uebd2<span class="fs3 ls1b wsb v1">\ued6f<span class="_2 blank"> </span>=<span class="_2 blank"> </span>\ue738\ue73d\ue74e\ued6b \ue732</span></div><div class="t m0 x15 h8 y2a ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x6 h9 y2b ff4 fs5 fc0 sc0 ls14">\uebd1<span class="fs3 ls1b wsb v1">\ued6f<span class="_8 blank"> </span>+<span class="_8 blank"> </span>\ue738\ue73d\ue74e \ued6b\ue732</span></div><div class="t m0 x30 h8 y2a ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x31 h10 y2b ff4 fs5 fc0 sc0 lsb">\uebd2<span class="fs3 ls1b wsc v1">\ued6f = <span class="v6">\ue74c</span></span></div><div class="t m0 x32 ha y2c ff4 fs5 fc0 sc0 ls3">\uebd1<span class="fs3 ls1b ws2 va">(<span class="wsd v4">1 \u2212 \ue74c</span></span></div><div class="t m0 x33 ha y2c ff4 fs5 fc0 sc0 ls3">\uebd1<span class="fs3 ls1b va">)</span></div><div class="t m0 x34 h13 y2d ff4 fs3 fc0 sc0 ls16">\ue74a<span class="ls17 v8">+</span><span class="ls1b vb">\ue74c</span></div><div class="t m0 x35 ha y2c ff4 fs5 fc0 sc0 lsb">\uebd2<span class="fs3 ls1b ws2 va">(<span class="wsd v4">1 \u2212 \ue74c</span></span></div><div class="t m0 x36 ha y2c ff4 fs5 fc0 sc0 ls6">\uebd2<span class="fs3 ls1b va">)</span></div><div class="t m0 x37 h8 y2d ff4 fs3 fc0 sc0 ls18">\ue749<span class="ff2 ls1b ws10 v8"> </span></div><div class="t m0 x1 h6 y2e ff2 fs3 fc1 sc0 ls1b ws10">Teorema: </div><div class="t m0 x1 h8 y2f ff2 fs3 fc0 sc0 ls1b ws10">Sejam <span class="_4 blank"> </span><span class="ff4 ls7">\ue73a</span> <span class="_4 blank"> </span>e <span class="_4 blank"> </span><span class="ff4 ls9">\ue73b</span> <span class="_4 blank"> </span>v.a\u2019s <span class="_4 blank"> </span>independentes <span class="_4 blank"> </span>com <span class="_4 blank"> </span>distri<span class="_5 blank"></span>buição <span class="_4 blank"> </span>Bernoulli <span class="_4 blank"> </span>de <span class="_4 blank"> </span>parâmetros <span class="_4 blank"> </span><span class="ff4">\ue74c</span></div><div class="t m0 x12 h9 y30 ff4 fs5 fc0 sc0 ls3">\uebd1<span class="ff2 fs3 ls1b ws10 v1"> <span class="_4 blank"> </span>e <span class="_4 blank"> </span><span class="ff4">\ue74c</span></span></div><div class="t m0 x13 hb y30 ff4 fs5 fc0 sc0 lsb">\uebd2<span class="ff2 fs3 ls1b ws10 v1">, </span></div><div class="t m0 x1 h8 y31 ff2 fs3 fc0 sc0 ls1b ws10">respectivamente. Se <span class="ff4 wse">\ue74a<span class="_2 blank"> </span>\u2192 \u221e</span> e <span class="ff4 wse">\ue749<span class="_1 blank"> </span>\u2192 \u221e</span>, então: </div><div class="t m0 x23 h8 y32 ff4 fs3 fc0 sc0 ls1b ws2">\ued6b\ue732</div><div class="t m0 x38 h8 y33 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x19 h9 y34 ff4 fs5 fc0 sc0 ls15">\uebd1<span class="fs3 ls1b ws9 v1">\u2212 \ue732</span></div><div class="t m0 x15 h8 y33 ff4 fs3 fc0 sc0 ls1b">\uede0</div><div class="t m0 x6 ha y34 ff4 fs5 fc0 sc0 ls6">\uebd2<span class="fs3 ls1b wsf v1">\ued6f \u2212 <span class="ws2 v2">(</span>\ue74c</span></div><div class="t m0 x39 h9 y34 ff4 fs5 fc0 sc0 ls13">\uebd1<span class="fs3 ls1b ws9 v1">\u2212 \ue74c</span></div><div class="t m0 x3a ha y34 ff4 fs5 fc0 sc0 ls6">\uebd2<span class="fs3 ls1b va">)</span></div><div class="t m0 x3b h14 y35 ff4 fs3 fc0 sc0 ls1b ws2">\ueda7<span class="vc">\ue74c</span></div><div class="t m0 x14 ha y36 ff4 fs5 fc0 sc0 ls3">\uebd1<span class="fs3 ls1b ws10 v1"> <span class="ws2 v2">(</span><span class="wsd">1 \u2212 \ue74c</span></span></div><div class="t m0 x3c ha y36 ff4 fs5 fc0 sc0 ls3">\uebd1<span class="fs3 ls1b va">)</span></div><div class="t m0 x3d h15 y37 ff4 fs3 fc0 sc0 ls19">\ue74a<span class="ls17 vd">+</span><span class="ls1b ve">\ue74c</span></div><div class="t m0 x39 ha y38 ff4 fs5 fc0 sc0 lsb">\uebd2<span class="fs3 ls1b ws10 v1"> <span class="ws2 v2">(</span><span class="wsd">1 \u2212 \ue74c</span></span></div><div class="t m0 x3e ha y38 ff4 fs5 fc0 sc0 lsb">\uebd2<span class="fs3 ls1b va">)</span></div><div class="t m0 x1d h16 y39 ff4 fs3 fc0 sc0 ls1a">\ue749<span class="ls1b ws10 vf">\u223c<span class="_2 blank"> </span>\ue730<span class="_0 blank"> </span>(0,<span class="_6 blank"> </span> 1)<span class="ff2"> </span></span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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