<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/a81faa3b-f28c-48ea-a234-22166789b4bd/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls13 wsb"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls13 wsb">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls13 wsb"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls13 wsb">Estatística Aplicada - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls13 wsb"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls13 wsb">DISTRIBUIÇÃO UNIFORME DISCRETA E </div><div class="t m0 x1 h5 y8 ff3 fs2 fc0 sc0 ls13 wsb">DISTRIBUIÇÃO DE BERNOULLI </div><div class="t m0 x1 h6 y9 ff3 fs3 fc1 sc0 ls13 wsb">Modelo/distribuição de probabilidade </div><div class="t m0 x1 h7 ya ff2 fs4 fc0 sc0 ls13 wsb">Define a v.a e sua distribuição. </div><div class="t m0 x3 h8 yb ff4 fs4 fc0 sc0 ls13 wsb">\ue72f\ue74b\ue740\ue741\ue748\ue74b \ue740\ue741</div><div class="t m0 x4 h9 yc ff4 fs4 fc0 sc0 ls13 ws0">\ue732\ue74e\ue74b\ue73e\ue73d\ue73e\ue745\ue748\ue745\ue740\ue73d\ue740\ue741 <span class="wsb v1">=<span class="_0 blank"> </span>\ue738<span class="_1 blank"> </span>.<span class="_2 blank"> </span>\ue723.<span class="_2 blank"> </span> + <span class="v1">\ue728\ue751\ue74a<span class="_1 blank"></span>çã\ue74b \ue740\ue741 \ue74c\ue74e\ue74b\ue73e\ue73d\ue73e\ue745\ue748\ue745\ue740\ue73d\ue740\ue741</span></span></div><div class="t m0 x5 ha yd ff4 fs4 fc0 sc0 ls13 wsb">\ue728\ue751\ue74açã\ue74b \ue740\ue741 \ue740\ue745\ue74f\ue750\ue74e\ue745\ue73e\ue751\ue745çã\ue74b<span class="_3 blank"> </span><span class="ls0 v2"> </span><span class="ff2 v2"> </span></div><div class="t m0 x1 h7 ye ff2 fs4 fc0 sc0 ls13 wsb"> </div><div class="t m0 x1 h6 yf ff3 fs3 fc1 sc0 ls13 wsb">Distribuição uniforme discreta </div><div class="t m0 x1 h8 y10 ff2 fs4 fc0 sc0 ls13 wsb">Seja uma v.a. <span class="ff4 ws1">\ue73a<span class="_1 blank"></span>: \u03a9<span class="_0 blank"> </span>\u27f6<span class="_0 blank"> </span>\u211d</span> discreta, com <span class="ff4 ls1">\u03a9</span> finito e equiprovável. A v.a X, que assume os </div><div class="t m0 x1 h8 y11 ff2 fs4 fc0 sc0 ls13 wsb">valores <span class="ff4">\ue754</span></div><div class="t m0 x6 hb y12 ff4 fs5 fc0 sc0 ls2">\ueb35<span class="fs4 ls13 ws2 v3">, \ue754</span>\ueb36<span class="fs4 ls13 ws2 v3">, \ue754<span class="_4 blank"></span><span class="fs5 ls2 v4">\ueb37<span class="fs4 ls13 ws3 v3">, \u2026 , \ue754</span><span class="ls3">\uebde<span class="ff2 fs4 ls13 wsb v3"> t<span class="_4 blank"></span>em distribuição uniforme discreta se sua função de </span></span></span></span></div><div class="t m0 x1 h7 y13 ff2 fs4 fc0 sc0 ls13 wsb">probabilidade é: </div><div class="t m0 x7 h8 y14 ff4 fs4 fc0 sc0 ls13">\ue74c</div><div class="t m0 x8 hc y15 ff4 fs5 fc0 sc0 ls4">\uebd1<span class="fs4 ls13 ws4 v5">(<span class="ls5 v6">\ue754</span><span class="ls6">)<span class="ls13 ws5 v6">= \ued5d<span class="v7">1</span></span></span></span></div><div class="t m0 x9 hd y16 ff4 fs4 fc0 sc0 ls7">\ue747<span class="ff2 ls13 wsb v8">, se </span><span class="ls13 ws6 v8">\ue754<span class="_5 blank"> </span>\u2208 {\ue754</span></div><div class="t m0 xa hb y17 ff4 fs5 fc0 sc0 ls2">\ueb35<span class="fs4 ls13 wsb v3">,<span class="_2 blank"> </span> \ue754</span><span class="ls8">\ueb36<span class="fs4 ls13 wsb v3">,<span class="_2 blank"> </span>\u2026<span class="_2 blank"> </span>,<span class="_2 blank"> </span> \ue754</span><span class="ls3">\uebde<span class="fs4 ls13 v3">}</span></span></span></div><div class="t m0 xb h8 y18 ff4 fs4 fc0 sc0 ls13 wsb">0 <span class="ff2">, caso contrário</span></div><div class="t m0 xc h7 y14 ff2 fs4 fc0 sc0 ls13 wsb"> </div><div class="t m0 x1 h8 y19 ff2 fs4 fc1 sc0 ls13 wsb">Notação: <span class="ff4 fc0 ws5">\ue73a<span class="_5 blank"> </span>\u223c \ue737{\ue754</span></div><div class="t m0 xd hb y1a ff4 fs5 fc0 sc0 ls2">\ueb35<span class="fs4 ls13 ws3 v3">, \u2026 , \ue754</span><span class="ls9">\uebe1<span class="fs4 ls13 ws4 v3">}<span class="_4 blank"></span><span class="ff2 wsb"> </span></span></span></div><div class="t m0 x1 h7 y1b ff2 fs4 fc1 sc0 ls13 wsb">Função de distribuição: </div><div class="t m0 xe h8 y1c ff4 fs4 fc0 sc0 ls13">\ue728</div><div class="t m0 xf he y1d ff4 fs5 fc0 sc0 ls4">\uebd1<span class="fs4 ls13 ws4 v5">(<span class="ls5 v6">\ue754</span><span class="lsa">)<span class="ls13 ws5 v6">= \ue732<span class="_1 blank"></span></span></span>(<span class="ws7 v6">\ue73a \u2264 \ue754<span class="_1 blank"> </span></span><span class="lsa">)</span><span class="ws8 v6">=<span class="_6 blank"> </span>\uedcd </span><span class="v9">1</span></span></div><div class="t m0 x10 h8 y1e ff4 fs4 fc0 sc0 ls13">\ue747</div><div class="t m0 x11 hf y1f ff4 fs5 fc0 sc0 lsb">\uebeb<span class="fs6 lsc va">\uecd4</span><span class="ls13 wsb"> \uebb8 \uebeb<span class="_7 blank"> </span><span class="ff2 fs4 v7"> </span></span></div><div class="t m0 x1 h7 y20 ff2 fs4 fc1 sc0 ls13 wsb">Esperança: </div><div class="t m0 x12 h10 y21 ff4 fs4 fc2 sc0 lsd">\ue727<span class="ls13 ws4 vb">[</span><span class="lse">\ue73a<span class="ls6 vb">]</span><span class="lsf">=<span class="fc0 ls13 vc">1</span></span></span></div><div class="t m0 x13 hd y22 ff4 fs4 fc0 sc0 ls10">\ue747<span class="ls13 ws9 v8">\uedcd \ue754<span class="fs5 v4">\uebdc</span></span></div><div class="t m0 x14 h11 y23 ff4 fs5 fc0 sc0 ls13">\uebde</div><div class="t m0 x15 hf y24 ff4 fs5 fc0 sc0 ls13 wsa">\uebdc \ueb40\ueb35<span class="_8 blank"> </span><span class="ff2 fs4 wsb v7"> </span></div><div class="t m0 x1 h7 y25 ff2 fs4 fc1 sc0 ls13 wsb">Variância: </div><div class="t m0 x16 h10 y26 ff4 fs4 fc0 sc0 ls13 wsb">\ue738\ue73d\ue74e <span class="ws4 vb">(</span><span class="lse">\ue73a<span class="ls6 vb">)</span><span class="lsf">=</span></span><span class="vc">1</span></div><div class="t m0 x17 hd y27 ff4 fs4 fc0 sc0 ls10">\ue747<span class="ls13 ws9 v8">\uedcd \ue754<span class="fs5 vd">\uebdc</span></span></div><div class="t m0 x5 h11 y28 ff4 fs5 fc0 sc0 ls13">\ueb36</div><div class="t m0 x18 h11 y29 ff4 fs5 fc0 sc0 ls13">\uebde</div><div class="t m0 xb h12 y2a ff4 fs5 fc0 sc0 ls13 wsa">\uebdc \ueb40\ueb35<span class="_9 blank"> </span><span class="fs4 ls11 v7">\u2212<span class="ls12 v0">\ued65<span class="ls13 vc">1</span></span></span></div><div class="t m0 x19 hd y27 ff4 fs4 fc0 sc0 ls7">\ue747<span class="ls13 wsb v8"> <span class="_2 blank"> </span>\uedcd<span class="_2 blank"> </span>\ue754<span class="fs5 v4">\uebdc</span></span></div><div class="t m0 x1a h11 y29 ff4 fs5 fc0 sc0 ls13">\uebde</div><div class="t m0 x1b h13 y2a ff4 fs5 fc0 sc0 ls13 wsa">\uebdc \ueb40\ueb35<span class="_8 blank"> </span><span class="fs4 ls1 v7">\ued69</span><span class="ve">\ueb36</span></div><div class="t m0 x1c h7 y26 ff2 fs4 fc0 sc0 ls13 wsb"> </div><div class="t m0 x1 h14 y2b ff3 fs4 fc2 sc0 ls13 wsb"> </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/a81faa3b-f28c-48ea-a234-22166789b4bd/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls13 wsb"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls13 wsb">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls13 wsb"> </div></div><div class="t m0 x1 h6 y2c ff3 fs3 fc1 sc0 ls13 wsb">Distribuição Bernoulli </div><div class="t m0 x1 h7 y2d ff2 fs4 fc0 sc0 ls13 wsb">Seja um experimento que tem dois resultados possív<span class="_4 blank"></span>eis: sucesso e fracasso. Defina a </div><div class="t m0 x1 h7 y2e ff2 fs4 fc0 sc0 ls13 wsb">v.a. X como sendo: </div><div class="t m0 x1d h15 y2f ff4 fs4 fc0 sc0 ls13 wsc">\ue73a<span class="_5 blank"> </span>=<span class="_0 blank"> </span>\ued5c <span class="ls1 v1">1</span><span class="ff2 wsb v1">, se sucesso oc</span><span class="ws4 v1">\ue74b\ue74e\ue74e\ue741</span></div><div class="t m0 x9 h8 y30 ff4 fs4 fc0 sc0 ls1">0<span class="ff2 ls13 wsb">, <span class="ff4">\ue73f\ue73d\ue74f\ue74b \ue73f\ue74b\ue74a\ue750\ue74eá\ue74e\ue745\ue74b </span><span class="v2"> </span></span></div><div class="t m0 x1 h16 y31 ff2 fs4 fc0 sc0 ls13 wsb">Considere que <span class="ff4 lse">\ue732<span class="ls13 ws4 vb">(<span class="v6">\ue735\ue751\ue73f\ue741\ue74f\ue74f\ue74b</span><span class="lsa">)</span></span><span class="ls13 ws5">= \ue732<span class="_1 blank"> </span><span class="ws4 vb">(</span>\ue73a<span class="_5 blank"> </span>= 1<span class="lsa vb">)</span>= \ue74c</span></span> e, po<span class="_1 blank"> </span>rtanto, <span class="ff4 lse">\ue732<span class="ls13 ws4 vb">(<span class="v6">\ue728\ue74e\ue73d\ue73f\ue73d\ue74f\ue74f\ue74b</span><span class="ls14">)</span></span><span class="ls13">=</span></span></div><div class="t m0 x1 h16 y32 ff4 fs4 fc0 sc0 lse">\ue732<span class="ls13 ws4 vb">(</span><span class="ls13 ws5">\ue73a<span class="_5 blank"> </span>= 0<span class="lsa vb">)</span><span class="wsd">=<span class="_0 blank"> </span>1 \u2212 \ue74c<span class="ff2 wsb">. </span></span></span></div><div class="t m0 x1 h7 y33 ff2 fs4 fc0 sc0 ls13 wsb">Então a função de probabilidade de X é dada por: </div><div class="t m0 x7 h8 y34 ff4 fs4 fc0 sc0 ls13">\ue74c</div><div class="t m0 x8 h17 y35 ff4 fs5 fc0 sc0 ls4">\uebd1<span class="fs4 ls13 ws4 v5">(<span class="ls5 v6">\ue754</span><span class="ls6">)<span class="ls13 ws5 v6">= \ued5c</span><span class="ls15 v2">\ue74c</span></span></span><span class="ls16 vf">\uebeb</span><span class="fs4 ls13 wsb v10"> <span class="ws4 vb">(</span><span class="wse">1 \u2212 \ue74c<span class="_1 blank"></span><span class="ws4 vb">)<span class="_4 blank"></span><span class="fs5 wsf v11">\ueb35\ueb3f\uebeb <span class="ff2 fs4 wsb v12"> , <span class="ff4 ws10">\ue754<span class="_5 blank"> </span>\u2208 {0,1}</span></span></span></span></span></span></div><div class="t m0 x1e h8 y36 ff4 fs4 fc0 sc0 ls1">0<span class="ff2 ls13 wsb"> , caso contrário <span class="_a blank"> </span><span class="v1"> </span></span></div><div class="t m0 x1 h8 y37 ff2 fs4 fc1 sc0 ls13 wsb">Notação: <span class="ff4 fc0 ws5">\ue73a<span class="_5 blank"> </span>\u223c \ue724\ue741\ue74e(\ue74c<span class="_1 blank"> </span>)</span><span class="fc0"> </span></div><div class="t m0 x1 h7 y38 ff2 fs4 fc1 sc0 ls13 wsb">Esperança: <span class="_b blank"> </span><span class="ff4 fc2 ls17 v13">\ue727<span class="ls13 ws4 vb">[</span><span class="lse">\ue73a<span class="lsa vb">]</span><span class="ls18">=<span class="fc0 ls19">\ue74c<span class="ff2 ls13"> </span></span></span></span></span></div><div class="t m0 x1 h7 y39 ff2 fs4 fc1 sc0 ls13 wsb">Variância: <span class="_c blank"> </span><span class="ff4 fc0 v13">\ue738\ue73d\ue74e <span class="ws4 vb">(</span><span class="lse">\ue73a<span class="ls6 vb">)</span><span class="ls13 ws11">=<span class="_0 blank"> </span>\ue74c<span class="_a blank"> </span>\u2212 \ue74c<span class="_1 blank"> </span><span class="fs5 ls1a v14">\ueb36</span></span></span>=<span class="_0 blank"> </span>\ue74c<span class="_1 blank"></span> (1 \u2212 \ue74c)<span class="ff2"> </span></span></div><div class="t m0 x1 h7 y3a ff2 fs4 fc0 sc0 ls13 wsb"> </div><div class="t m0 x1 h18 y3b ff2 fs0 fc0 sc0 ls13 wsb"> </div><div class="t m0 x1 h18 y3c ff2 fs0 fc0 sc0 ls13 wsb"> </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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