<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/d8fb939f-d8e7-42c0-aa6b-e6e90f6a2e2f/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls17 ws6"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls17 ws6">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls17 ws6"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls17 ws6">Estatística Aplicada - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls17 ws6"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls17 ws6">DISTRIBUIÇÕES QUI-QUADRADO, T-</div><div class="t m0 x1 h5 y8 ff3 fs2 fc0 sc0 ls17 ws6">STUDENT E F-SNEDECOR </div><div class="t m0 x1 h6 y9 ff3 fs3 fc1 sc0 ls17 ws6">Distribuição Qui-Quadrado </div><div class="t m0 x1 h7 ya ff2 fs4 fc0 sc0 ls17 ws6">Seja <span class="ff4 ws0">\ue73a<span class="_0 blank"> </span>\u223c \ue729\ue73d\ue749\ue73d<span class="_1 blank"> </span>\uf240\ue7d9<span class="_0 blank"> </span>= <span class="fs5 v1">\uebe1</span></span></div><div class="t m0 x3 h8 yb ff4 fs5 fc0 sc0 ls0">\ueb36<span class="fs4 ls17 ws1 v2">, \ue7da<span class="_0 blank"> </span>=<span class="_2 blank"> </span></span><span class="ls17 v3">\ueb35</span></div><div class="t m0 x4 h8 yb ff4 fs5 fc0 sc0 ls17 ws2">\ueb36<span class="fs4 ws3 v2">\uf241<span class="ff2 ws6">. Então <span class="ff4 ls1">\ue73a</span> tem distribuição Qui-quadrado com n graus </span></span></div><div class="t m0 x1 h9 yc ff2 fs4 fc0 sc0 ls17 ws6">de liberdade e sua densidade é dada por: </div><div class="t m0 x5 h7 yd ff4 fs4 fc0 sc0 ls17">\ue742</div><div class="t m0 x6 ha ye ff4 fs5 fc0 sc0 ls2">\uebd1<span class="fs4 ls17 ws3 v4">(<span class="ls3 v5">\ue754</span><span class="ls4">)<span class="ls17 v5">=</span></span></span></div><div class="c x7 yf w3 hb"><div class="t m0 x0 h7 y10 ff4 fs4 fc0 sc0 ls17">\u23a9</div></div><div class="c x7 y11 w4 hc"><div class="t m0 x0 h7 y12 ff4 fs4 fc0 sc0 ls17">\u23aa</div></div><div class="c x7 y13 w5 hd"><div class="t m0 x0 h7 y12 ff4 fs4 fc0 sc0 ls17">\u23a8</div></div><div class="c x7 y14 w4 hc"><div class="t m0 x0 h7 y12 ff4 fs4 fc0 sc0 ls17">\u23aa</div></div><div class="c x7 y15 w6 he"><div class="t m0 x0 h7 y16 ff4 fs4 fc0 sc0 ls17">\u23a7</div></div><div class="t m0 x8 hf y17 ff4 fs4 fc0 sc0 ls5">\uf240<span class="ls17 v1">1</span></div><div class="t m0 x9 h10 y18 ff4 fs4 fc0 sc0 ls6">2<span class="ls17 ws3 v2">\uf241<span class="fs5 v6">\uebe1</span></span></div><div class="t m0 xa h11 y19 ff4 fs5 fc0 sc0 ls7">\ueb36<span class="fs4 ls17 ws6 v7"> \ue754<span class="_3 blank"> </span></span><span class="ls8 v8">\uf240</span><span class="ls17 v4">\uebe1</span></div><div class="t m0 xb h12 y1a ff4 fs5 fc0 sc0 ls9">\ueb36<span class="ls17 ws4 v9">\uf241\ueb3f\ueb35 </span><span class="fs4 ls17 ws6 va"> \ue741<span class="_3 blank"> </span></span><span class="lsa vb">\ueb3f</span><span class="ls17 vc">\uebeb</span></div><div class="t m0 xc h13 y1b ff4 fs5 fc0 sc0 lsb">\ueb36<span class="fs4 ls17 ws6 vd"> </span></div><div class="t m0 xd hf y1c ff4 fs4 fc0 sc0 ls17 ws5">\u0393 \uf240<span class="v1">\ue74a</span></div><div class="t m0 xe h14 y1d ff4 fs4 fc0 sc0 lsc">2<span class="lsd v2">\uf241</span><span class="ls17 ws6 ve">,<span class="_4 blank"> </span> \ue754<span class="_0 blank"> </span>><span class="_2 blank"> </span>0</span></div><div class="t m0 xf h7 y1e ff4 fs4 fc0 sc0 ls17 ws6">0,<span class="_4 blank"> </span> <span class="ff2"> caso contrário</span></div><div class="t m0 x10 h9 yd ff2 fs4 fc0 sc0 ls17 ws6"> </div><div class="t m0 x1 h7 y1f ff2 fs4 fc1 sc0 ls17 ws6">Notação: <span class="ff4 fc0 ws0">\ue73a<span class="_0 blank"> </span>\u223c \ue7ef<span class="_5 blank"></span><span class="fs5 v8">\uebe1</span></span></div><div class="t m0 x11 h15 y20 ff4 fs5 fc0 sc0 lse">\ueb36<span class="ff3 fs4 fc2 ls17 ws6 vf"> </span></div><div class="t m0 x1 h16 y21 ff2 fs4 fc1 sc0 ls17 ws6">Esperança: <span class="ff4 fc0 lsf">\ue727<span class="ls17 ws3 v10">[</span><span class="ls1">\ue73a<span class="ls4 v10">]</span><span class="ls10">=<span class="fs5 ls17 v1">\uec08</span></span></span></span></div><div class="t m0 x12 h17 y22 ff4 fs5 fc0 sc0 ls11">\uec09<span class="fs4 ls12 v2">=</span><span class="fs6 ls17 v11">\uecd9</span></div><div class="t m0 x13 h18 y23 ff4 fs6 fc0 sc0 ls17">\uec2e</div><div class="t m0 x13 h18 y24 ff4 fs6 fc0 sc0 ls17">\uec2d</div><div class="t m0 x13 h19 y25 ff4 fs6 fc0 sc0 ls13">\uec2e<span class="fs4 ls17 ws0 v12">= \ue74a<span class="ff2 ws6">. </span></span></div><div class="t m0 x1 h16 y26 ff2 fs4 fc1 sc0 ls17 ws6">Variância: <span class="ff4 fc0 ws3">\ue738\ue73d\ue74e<span class="_6 blank"></span><span class="v10">(</span><span class="ls1">\ue73a<span class="ls4 v10">)</span><span class="ls14">=</span></span><span class="fs5 v1">\uec08</span></span></div><div class="t m0 x14 h17 y27 ff4 fs5 fc0 sc0 ls15">\uec09<span class="fs6 ls16 v13">\uec2e</span><span class="fs4 ls12 v2">=</span><span class="fs6 ls17 v11">\uecd9</span></div><div class="t m0 x15 h18 y28 ff4 fs6 fc0 sc0 ls17">\uec2e</div><div class="t m0 x15 h18 y29 ff4 fs6 fc0 sc0 ls17">\uec2d</div><div class="t m0 x15 h19 y2a ff4 fs6 fc0 sc0 ls13">\uec30<span class="fs4 ls17 ws0 v12">= 2\ue74a<span class="ff2 ws6">. </span></span></div><div class="t m0 x1 h9 y2b ff2 fs4 fc1 sc0 ls17 ws6">Tabela: </div><div class="t m0 x16 h9 y2c ff2 fs4 fc0 sc0 ls17 ws6"> </div><div class="t m0 x1 h9 y2d ff2 fs4 fc0 sc0 ls17 ws6"> </div><div class="t m0 x1 h6 y2e ff3 fs3 fc1 sc0 ls17 ws6">Distribuição t-Student </div><div class="t m0 x1 h7 y2f ff2 fs4 fc0 sc0 ls17 ws6">Seja <span class="ff4 ls1">\ue73a</span> v.a contínua. Dizemos que <span class="ff4 ls1">\ue73a</span> tem distribuição t-Studen com n graus de </div><div class="t m0 x1 h9 y30 ff2 fs4 fc0 sc0 ls17 ws6">liberdade se sua densidade é dada por: </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/d8fb939f-d8e7-42c0-aa6b-e6e90f6a2e2f/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls17 ws6"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls17 ws6">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls17 ws6"> </div></div><div class="t m0 x17 h7 y31 ff4 fs4 fc0 sc0 ls17">\ue742</div><div class="t m0 x18 h1a y32 ff4 fs5 fc0 sc0 ls18">\uebd1<span class="fs4 ls17 ws3 v4">(<span class="ls3 v5">\ue754</span><span class="ls4">)<span class="ls19 v5">=</span><span class="ls17 ws7 v12">\u0393 \uf240<span class="ws8 v1">\ue74a + 1</span></span></span></span></div><div class="t m0 x19 h8 y33 ff4 fs4 fc0 sc0 ls1a">2<span class="ls17 v2">\uf241</span></div><div class="t m0 x4 hf y34 ff4 fs4 fc0 sc0 ls17 ws9">\u0393 \uf240<span class="v1">\ue74a</span></div><div class="t m0 x19 h1b y35 ff4 fs4 fc0 sc0 lsc">2<span class="ls1b v2">\uf241</span><span class="ls17 v14">1</span></div><div class="t m0 x1a h1c y36 ff4 fs4 fc0 sc0 ls17 ws3">\u221a<span class="ws6 v10">\ue74a \ue7e8<span class="_1 blank"> </span><span class="v15"> <span class="_4 blank"> </span>\uf246</span></span><span class="ls1c v16">\ue754</span><span class="fs5 v17">\ueb36</span></div><div class="t m0 x1b h1d y37 ff4 fs4 fc0 sc0 ls1d">\ue74a<span class="ls6 wsa v18">+ 1\uf247</span><span class="fs5 ls17 ws2 v19">\ueb3f<span class="ls1e v1a">(</span><span class="v1b">\uebe1\ueb3e\ueb35<span class="v10">)</span></span></span></div><div class="t m0 x1c h15 y38 ff4 fs5 fc0 sc0 ls1f">\ueb36<span class="fs4 ls17 ws6 v1c">,<span class="_4 blank"> </span> \ue754<span class="_0 blank"> </span>\u2208<span class="_2 blank"> </span>\u211d<span class="ff2"> </span></span></div><div class="t m0 x1 h9 y39 ff2 fs4 fc1 sc0 ls17 ws6"> </div><div class="t m0 x1 h7 y3a ff2 fs4 fc1 sc0 ls17 ws6">Notação: <span class="ff4 fc0 ws0">\ue73a<span class="_0 blank"> </span>\u223c \ue750<span class="fs5 ls20 v8">\uebe1</span></span><span class="ff3 fc2"> </span></div><div class="t m0 x1 h16 y3b ff2 fs4 fc1 sc0 ls17 ws6">Esperança: <span class="ff4 fc0 lsf">\ue727<span class="ls17 ws3 v10">[</span><span class="ls1">\ue73a<span class="ls4 v10">]</span><span class="ls17 ws0">= 0</span></span></span><span class="fc0">, se <span class="ff4 wsb">\ue74a \u2265 2</span>. </span></div><div class="t m0 x1 h16 y3c ff2 fs4 fc1 sc0 ls17 ws6">Variância: <span class="ff4 fc0 ws3">\ue738\ue73d\ue74e<span class="_6 blank"></span><span class="v10">(</span><span class="ls1">\ue73a<span class="ls4 v10">)</span><span class="ls21">=</span></span><span class="fs5 v1">\uebe1</span></span></div><div class="t m0 x14 h8 y3d ff4 fs5 fc0 sc0 ls17 wsc">\uebe1\ueb3f\ueb36 <span class="fs4 wsd v2">, \ue74a<span class="_2 blank"> </span>\u2265<span class="_2 blank"> </span>3<span class="ff2 ws6">. </span></span></div><div class="t m0 x1 h9 y3e ff2 fs4 fc0 sc0 ls17 ws6"> </div><div class="t m0 x1 h7 y3f ff2 fs4 fc1 sc0 ls17 wse">Resultado:<span class="fc2 ws6"> Se <span class="ff4 wsf">\ue74a \u2192 \u221e</span>, e<span class="_6 blank"> </span>ntão <span class="ff4 ws0">\ue73a<span class="_2 blank"> </span>\u223c \ue750<span class="fs5 ls22 v8">\uebe1</span><span class="wsf">\u2192 \ue73c<span class="_0 blank"> </span>\u223c \ue730<span class="_6 blank"></span>(0,1)</span></span><span class="ls6">.</span><span class="ff3"> </span></span></div><div class="t m0 x1 h6 y40 ff3 fs3 fc1 sc0 ls17 ws6"> </div><div class="t m0 x1 h6 y41 ff3 fs3 fc1 sc0 ls17 ws6">Distribuição F-Snedecor </div><div class="t m0 x1 h7 y42 ff2 fs4 fc0 sc0 ls17 ws6">Seja <span class="ff4 ls1">\ue73a</span> v.a contínua. Dizemos que <span class="ff4 ls1">\ue73a</span> tem distribuição F-Snedecor com n e m graus de </div><div class="t m0 x1 h9 y43 ff2 fs4 fc0 sc0 ls17 ws6">liberdade se sua densidade é dada por: </div><div class="t m0 x1d h7 y44 ff4 fs4 fc2 sc0 ls17">\ue742</div><div class="t m0 x1e ha y45 ff4 fs5 fc2 sc0 ls2">\uebd1<span class="fs4 ls17 ws3 v4">(<span class="ls3 v5">\ue754</span><span class="ls23">)<span class="ls17 v5">=</span></span></span></div><div class="c x1f y46 w7 hb"><div class="t m0 x0 h7 y10 ff4 fs4 fc2 sc0 ls17">\u23a9</div></div><div class="c x1f y47 w7 hc"><div class="t m0 x0 h7 y12 ff4 fs4 fc2 sc0 ls17">\u23aa</div></div><div class="c x1f y48 w7 hd"><div class="t m0 x0 h7 y12 ff4 fs4 fc2 sc0 ls17">\u23a8</div></div><div class="c x1f y49 w7 hc"><div class="t m0 x0 h7 y12 ff4 fs4 fc2 sc0 ls17">\u23aa</div></div><div class="c x1f y4a w7 he"><div class="t m0 x0 h7 y16 ff4 fs4 fc2 sc0 ls17">\u23a7</div></div><div class="t m0 x13 hf y4b ff4 fs4 fc2 sc0 ls17 ws9">\u0393 \uf240<span class="ws8 v1">\ue74a + \ue749</span></div><div class="t m0 x20 h1e y4c ff4 fs4 fc2 sc0 ls24">2<span class="ls25 ws6 v2">\uf241 \uf240<span class="_5 blank"></span><span class="ls17 v1">\ue74a</span></span></div><div class="t m0 x1a h1f y4c ff4 fs4 fc2 sc0 ls26">\ue749<span class="ls17 ws3 v2">\uf241<span class="fs5 v1d">\uebe1</span></span></div><div class="t m0 x21 h15 y4d ff4 fs5 fc2 sc0 ls17">\ueb36</div><div class="t m0 x15 hf y4e ff4 fs4 fc2 sc0 ls17 ws9">\u0393 \uf240<span class="v1">\ue74a</span></div><div class="t m0 x22 h1e y4f ff4 fs4 fc2 sc0 lsc">2<span class="ls17 ws7 v2">\uf241 \u0393 \uf240<span class="v1">\ue749</span></span></div><div class="t m0 x23 h20 y4f ff4 fs4 fc2 sc0 ls27">2<span class="ls28 v2">\uf241</span><span class="ls17 ws6 ve"> \ue754<span class="_3 blank"> </span><span class="fs5 v1e">\uebe1</span></span></div><div class="t m0 xe h21 y50 ff4 fs5 fc2 sc0 ls9">\ueb36<span class="ls17 ws10 v9">\ueb3f\ueb35 </span><span class="fs4 ls17 ws6 vd"> <span class="_4 blank"> </span>\uf240<span class="_7 blank"> </span><span class="vc">\ue74a</span></span></div><div class="t m0 x24 h22 y51 ff4 fs4 fc2 sc0 ls29">\ue749<span class="ls17 ws8 v18">\ue754<span class="_8 blank"> </span>+ 1\uf241</span><span class="fs5 ls17 ws2 v11">\ueb3f<span class="v1b">\uebe1\ueb3e\uebe0</span></span></div><div class="t m0 x25 h23 y52 ff4 fs5 fc2 sc0 ls2a">\ueb36<span class="fs4 ls17 ws6 v1f">,<span class="_4 blank"> </span> \ue754<span class="_0 blank"> </span>><span class="_2 blank"> </span>0</span></div><div class="t m0 x26 h7 y53 ff4 fs4 fc2 sc0 ls17 ws6">0 ,<span class="_4 blank"> </span> <span class="ff2"> caso contrário</span></div><div class="t m0 x27 h24 y44 ff3 fs4 fc2 sc0 ls17 ws6"> </div><div class="t m0 x1 h9 y54 ff2 fs4 fc1 sc0 ls17 ws6"> </div><div class="t m0 x1 h7 y55 ff2 fs4 fc1 sc0 ls17 ws6">Notação: <span class="ff4 fc0 ws0">\ue73a<span class="_0 blank"> </span>\u223c \ue728</span></div><div class="t m0 x28 h15 y56 ff4 fs5 fc0 sc0 ls17 ws11">\uebe1,\uebe0 <span class="ff3 fs4 fc2 ws6 v13"> </span></div><div class="t m0 x1 h16 y57 ff2 fs4 fc1 sc0 ls17 ws6">Esperança: <span class="ff4 fc0 lsf">\ue727<span class="ls17 ws3 v10">[</span><span class="ls1">\ue73a<span class="ls4 v10">]</span><span class="ls2b">=<span class="fs5 ls17 v1">\uebe1</span></span></span></span></div><div class="t m0 x12 h8 y58 ff4 fs5 fc0 sc0 ls17 ws2">\uebe1\ueb3f\ueb36<span class="ff2 fs4 ws6 v2">, se <span class="ff4 ws12">\ue74a \u2265 3</span>. </span></div><div class="t m0 x1 h16 y59 ff2 fs4 fc1 sc0 ls17 ws6">Variância: <span class="ff4 fc0 ws3">\ue738\ue73d\ue74e<span class="_6 blank"></span><span class="v10">(</span><span class="ls1">\ue73a<span class="ls4 v10">)</span><span class="ls2c">=</span></span><span class="fs5 ws2 v1">\ueb36\uebe1</span><span class="fs6 ls2d v20">\uec2e</span><span class="fs5 ls1e v21">(</span><span class="fs5 ws2 v1">\uebe0\ueb3e\uebe1<span class="_6 blank"> </span>\ueb3f\ueb36<span class="v10">)</span></span></span></div><div class="t m0 x14 h8 y5a ff4 fs5 fc0 sc0 ls17 ws6"> \uebe0<span class="ls1e v10">(</span><span class="ws2">\uebe1<span class="_6 blank"></span>\ueb3f\ueb36<span class="ls1e v10">)</span><span class="fs6 ls2d v13">\uec2e</span><span class="ws13">(\uebe0\ueb3f\ueb38) </span></span><span class="fs4 v2"> ,<span class="_4 blank"> </span> \ue74a<span class="_2 blank"> </span>\u2265<span class="_2 blank"> </span>3,<span class="_4 blank"> </span> \ue749<span class="_0 blank"> </span>\u2265<span class="_2 blank"> </span>5<span class="ff2 ls6">.<span class="ff5 ls17"> </span></span></span></div><div class="t m0 x1 h9 y5b ff2 fs4 fc0 sc0 ls17 ws6"> </div><div class="t m0 x1 h7 y5c ff2 fs4 fc1 sc0 ls17 wse">Resultado:<span class="fc2 ws6"> <span class="fc0 ls6">Se <span class="ff4 ls17 ws0">\ue736 \u223c \ue750<span class="fs5 ls2e v8">\uebe0</span></span><span class="ls17">, então <span class="ff4 ls2f">\ue736<span class="fs5 ls30 v9">\ueb36</span><span class="ls17 ws0">\u223c \ue728</span></span></span></span></span></div><div class="t m0 x29 h15 y5d ff4 fs5 fc0 sc0 ls17 ws14">\ueb35,\uebe0 <span class="ff3 fs4 fc2 ws6 v13"> </span></div><div class="t m0 x1 h25 y5e ff2 fs0 fc0 sc0 ls17 ws6"> </div><div class="t m0 x1 h25 y5f ff2 fs0 fc0 sc0 ls17 ws6"> </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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