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‎changelog/index.html

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<h2 id="2025">2025 年<a class="headerlink" href="#2025" title="Permanent link"></a></h2>
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<li><span style="font-family: var(--md-code-font-family)">01-05 <a href="https://github.com/ZJU-Turing/TuringCourses/commit/98380c50039cbfbe543c93e6bafb2aa93f0a8344">98380c5</a> </span>docs: 更新概率论 2024 秋冬小测题目 (<a href="https://github.com/ZJU-Turing/TuringCourses/pull/205">#205</a>)</li>
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<h2 id="2024">2024 年<a class="headerlink" href="#2024" title="Permanent link"></a></h2>
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<li><span style="font-family: var(--md-code-font-family)">09-20 <a href="https://github.com/ZJU-Turing/TuringCourses/commit/ffa07d3812d56a1f9f465f5cc650bac9b28088fb">ffa07d3</a> </span>更新短学期课程导航页 (<a href="https://github.com/ZJU-Turing/TuringCourses/pull/201">#201</a>)<ul>

‎major_elective/computer_vision/index.html

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<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M21 13.1c-.1 0-.3.1-.4.2l-1 1 2.1 2.1 1-1c.2-.2.2-.6 0-.8l-1.3-1.3c-.1-.1-.2-.2-.4-.2m-1.9 1.8-6.1 6V23h2.1l6.1-6.1-2.1-2M12.5 7v5.2l4 2.4-1 1L11 13V7h1.5M11 21.9c-5.1-.5-9-4.8-9-9.9C2 6.5 6.5 2 12 2c5.3 0 9.6 4.1 10 9.3-.3-.1-.6-.2-1-.2s-.7.1-1 .2C19.6 7.2 16.2 4 12 4c-4.4 0-8 3.6-8 8 0 4.1 3.1 7.5 7.1 7.9l-.1.2v1.8Z"></path></svg></span> 2024-07-04  <span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"></path></svg></span> Contributors <span class="contributors"><a href="https://github.com/TonyCrane" target="_blank" title="TonyCrane"><img alt="TonyCrane" src="https://avatars.githubusercontent.com/u/44120331"/></a><a href="https://github.com/ZhouTimeMachine" target="_blank" title="ZhouTimeMachine"><img alt="ZhouTimeMachine" src="https://avatars.githubusercontent.com/u/99057383"/></a><a href="https://github.com/Yusux" target="_blank" title="Yusux"><img alt="Yusux" src="https://avatars.githubusercontent.com/u/72163724"/></a><a href="https://github.com/mini-full" target="_blank" title="mini-full"><img alt="mini-full" src="https://avatars.githubusercontent.com/u/53207038"/></a><a href="https://github.com/GoldfishHorse" target="_blank" title="GoldfishHorse"><img alt="GoldfishHorse" src="https://avatars.githubusercontent.com/u/104991291"/></a></span></p>
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<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M21 13.1c-.1 0-.3.1-.4.2l-1 1 2.1 2.1 1-1c.2-.2.2-.6 0-.8l-1.3-1.3c-.1-.1-.2-.2-.4-.2m-1.9 1.8-6.1 6V23h2.1l6.1-6.1-2.1-2M12.5 7v5.2l4 2.4-1 1L11 13V7h1.5M11 21.9c-5.1-.5-9-4.8-9-9.9C2 6.5 6.5 2 12 2c5.3 0 9.6 4.1 10 9.3-.3-.1-.6-.2-1-.2s-.7.1-1 .2C19.6 7.2 16.2 4 12 4c-4.4 0-8 3.6-8 8 0 4.1 3.1 7.5 7.1 7.9l-.1.2v1.8Z"></path></svg></span> 2024-07-04  <span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"></path></svg></span> Contributors <span class="contributors"><a href="https://github.com/kxwangzju" target="_blank" title="kxwangzju"><img alt="kxwangzju" src="https://avatars.githubusercontent.com/u/53207038"/></a><a href="https://github.com/TonyCrane" target="_blank" title="TonyCrane"><img alt="TonyCrane" src="https://avatars.githubusercontent.com/u/44120331"/></a><a href="https://github.com/ZhouTimeMachine" target="_blank" title="ZhouTimeMachine"><img alt="ZhouTimeMachine" src="https://avatars.githubusercontent.com/u/99057383"/></a><a href="https://github.com/Yusux" target="_blank" title="Yusux"><img alt="Yusux" src="https://avatars.githubusercontent.com/u/72163724"/></a><a href="https://github.com/GoldfishHorse" target="_blank" title="GoldfishHorse"><img alt="GoldfishHorse" src="https://avatars.githubusercontent.com/u/104991291"/></a></span></p>
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‎math_phys/probability/概率论2024秋冬小测.pdf

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‎math_phys/probability/概率论2024秋冬小测.typ

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#import "@preview/numbly:0.1.0": *
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#set enum(full: true, numbering: numbly("{1:一、}", "({2})",))
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#set text(size: 14pt, font: "Source Han Serif SC")
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#let title(body, lev:1) = {
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show heading.where(level: lev): it => [
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#set align(center)
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#if lev == 1 {
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text(size: 22pt, font: "Source Han Serif SC")[#it.body]
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} else if lev == 2 {
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text(size: 18pt, font: "FZXiaoBiaoSong-B05S")[#it.body]
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}
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]
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heading(body, level: lev)
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}
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#title(lev: 1)[概率论（H）2023-2024 秋冬小测]
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#align(center)[#text(size: 15pt,font: "Ink Free",[shrike505])]
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#title(lev: 2)[第一次小测：2024年10月11日]
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+
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+ 假设事件 $A, B, C$ 互不相容，且 $P(A) = P(B) = 0.2, P(C) = 0.4$. 求 $P(A dash.en(C) union B)$.
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+ 假设事件 $A, B$ 相互独立，且 $P(A) = 0.6, P(B) = 0.3$. 求 $A$ 与 $B$ 至少有一个发生的条件下 $A$ 发生的概率.
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+ 对随机事件 $A, B$，若 $P(A bar B) = 0.2, P(dash.en(A) bar dash.en(B)) = 0.3, P(B) = 0.4$，求 $P(B bar A)$.
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+ 在线段 $A B$ 中随机取三点 $C, D, E$, 求三线段 $A C, A D, A E$ 可构成三角形的概率.
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+ 投票选举甲乙两人，已知甲共得 $m$ 张，乙共得 $n$ 张，$m gt.eq n + 2$. 求在第一张票后的计票过程中，甲得票数始终至少领先乙得票数 $2$ 张的概率.
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#title(lev: 2)[第二次小测：2024年11月22日]
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+ 设随机变量 $xi_1, xi_2, dots, xi_n$ 相互独立，且同分布. $P(xi_1 = i) = frac(2, 3^i), i = 1, 2, dots, n$. 令 $eta = min_(1 lt.eq k lt.eq n) xi_k$
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+ 求 $P(eta gt.eq i)$.
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+ 求 $eta$ 的分布列.
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+ 设 $X, Y$ 为非负整数值随机变量，$X + Y tilde P(lambda)$（泊松分布），并在给定 $X + Y = n$ 的条件下，$X tilde B(n, p)$. 求 $X, Y$ 的分布.
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+ 设随机变量 $X_1, X_2, X_3$ 相互独立，都服从参数为 1 的指数分布，
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记 $Y_1 = frac(X_1, X_1 + X_2), Y_2 = frac(X_1 + X_2, X_1 + X_2 + X_3), Y_3 = X_1 + X_2 + X_3$.
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+ 求 $(Y_1, Y_2, Y_3)$ 的联合密度函数.
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+ 证明 $Y_1, Y_2, Y_3$ 相互独立.

‎search/search_index.json

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