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数学代写|Math 130A Introduction to probability and stochastic porcesses Assignment 3

这是Math 130A, Introduction to probability and stochastic porcesses的一次作业分析

问题 1.

(1). If you roll a regular dice twice, what is the probability that the first outcome is 3 given that the sum of the outcomes is $8 ?$
(2). If you toss a fair coin twice, given that one of the outcome is head, what is the probability that the other outcome is head?
(3). If you roll a regular dice twice, what is the probability that one of the outcome is 6 given that the outcomes are different?

此题是一个离散概率空间的counting问题,掌握了概念很简单。

问题 2.

Suppose we have 12 women and 4 men. If we divide these 16 people into 4 groups of size $4,$ what is the probability that each group contains a man?

此题在counting的基础上加了点排列与组合,本质上巧妙的利用对称性即可解决。

问题 3.

Suppose $n>m$. Let $\mathcal{S}$ be the collection of all functions from $[n]$ to $[\mathrm{m}]$. We randomly pick a function $f$ from $\mathcal{S}$. Define event $A=\{f$ is surjective $\}$.
(1). Find $\mathbb{P}[A]$
(2). What is the limit of $\mathbb{P}[A]$ as $n \rightarrow \infty$ and $m$ is fixed?

仍然是利用对称性counting,然后加一点点极限的概念。

问题 4.

 Suppose we have a test for a certain disease. If a person has the disease, the test has $95 \%$ chance to be positive. If a person is healthy, the test has $5 \%$ chance to give a false positive result. Given that the test for a person is positive, what is the probability that the person has the disease?

标准的假设检验的问题。

问题 5.

Problem $5 .$ Let $A$ and $B$ be events such $0<\mathbb{P}[B]<1$ and $0<\mathbb{P}[A]<1$.
(1). Prove that $\mathbb{P}[A \mid B]>\mathbb{P}[A]$ if and only if $\mathbb{P}[B \mid A]>\mathbb{P}[B]$.
(2). Prove that $\mathbb{P}[A \mid B]>\mathbb{P}[A]$ if and only if $\mathbb{P}\left[A \mid B^{C}\right]<\mathbb{P}[A]$
(3). Let $S=\{1, \cdots, n\}$. If we pick two numbers from $S$ with replacement. Let $E=\{$ the first pick is an even number $\}, F=\{$ the sum of two numbers is even $\}$. When is $\mathbb{P}[F \mid E]<\mathbb{P}[F] ?$

在Math 130A中我们会学贝叶斯公式,此题可以用贝叶斯公式加一点点条件概率的变形得到证明。


Math 130A

Introduction to probability and stochastic porcesses

上课听不懂lecturer ?

笔记也看不懂?

Theory 太多 …Practice题目有点hold 不住?

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STATS 101代写请认准UpriviateTA

Math 130代写,stochastic porcesses代写, probability代写请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。

关于Math 130A的更多内容请参阅一份Math130代写.

抽象代数代写可以参考一份抽象代数代写案例

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