# on 02-Jan-2024 (Tue)

#### Annotation 7609073929484

 随机过程的期望值 For any random process $$X_{t}$$, the Expected Value is $$\mathbf{E}[X_{t}]=\int_{\Omega}X_{t}(\alpha)P(d\alpha)=\int_\mathbb{R}x\mu_{t}(dx)$$

#### Flashcard 7609075764492

Question
For any random process $$X_{t}$$, the Expected Value is [...]
$$\mathbf{E}[X_{t}]=\int_{\Omega}X_{t}(\alpha)P(d\alpha)=\int_\mathbb{R}x\mu_{t}(dx)$$

status measured difficulty not learned 37% [default] 0

For any random process $$X_{t}$$, the Expected Value is $$\mathbf{E}[X_{t}]=\int_{\Omega}X_{t}(\alpha)P(d\alpha)=\int_\mathbb{R}x\mu_{t}(dx)$$

#### Annotation 7609077337356

 随机过程的方差 For any random process $$X_{t}$$, the Varience is $$\operatorname{Var}[X_{t}]=\mathbf{E}[(X_{t}-\mathbf{E}[X_{t}])^{2}]$$

#### Flashcard 7609079172364

Question
For any random process $$X_{t}$$, the Varience is [...]
$$\operatorname{Var}[X_{t}]=\mathbf{E}[(X_{t}-\mathbf{E}[X_{t}])^{2}]$$

status measured difficulty not learned 37% [default] 0

For any random process $$X_{t}$$, the Varience is $$\operatorname{Var}[X_{t}]=\mathbf{E}[(X_{t}-\mathbf{E}[X_{t}])^{2}]$$

#### Annotation 7609080745228

 随机过程的自相关函数 For any random process $$X_{t}$$, the Autocorrelation at time instants $$t_{1}$$ and $$t_{2}$$ is: $$\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})$$ where $$\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})$$ is a joint probability distribution.

#### Flashcard 7609082580236

Question
For any random process $$X_{t}$$, the Autocorrelation at time instants $$t_{1}$$ and $$t_{2}$$ is: [...]

$$\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})$$

where $$\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})$$ is a joint probability distribution.

status measured difficulty not learned 37% [default] 0

For any random process $$X_{t}$$, the Autocorrelation at time instants $$t_{1}$$ and $$t_{2}$$ is: $$\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})$$ where $$\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})$$ is a joint probability distribution.

#### Annotation 7609091493132

 稳态信号条件 The process $$X_{t}$$ is said to be stationary if for any $$t_{1},t_{2},t_{3}, . . .$$ and $$τ$$, $$\mu_{t_{1},t_{2},t_{3},\cdots}=\mu_{t_{1}+\tau,t_{2}+\tau,t_{3}+\tau,\cdots}$$

#### Flashcard 7609093590284

Question

The process $$X_{t}$$ is said to be stationary if [...]

for any $$t_{1},t_{2},t_{3}, . . .$$ and $$τ$$, $$\mu_{t_{1},t_{2},t_{3},\cdots}=\mu_{t_{1}+\tau,t_{2}+\tau,t_{3}+\tau,\cdots}$$

status measured difficulty not learned 37% [default] 0

The process $$X_{t}$$ is said to be stationary if for any $$t_{1},t_{2},t_{3}, . . .$$ and $$τ$$, $$\mu_{t_{1},t_{2},t_{3},\cdots}=\mu_{t_{1}+\tau,t_{2}+\tau,t_{3}+\tau,\cdots}$$

#### Annotation 7609095163148

 广义稳态信号条件 The process $$X_{t}$$ is said to be wide sense stationary (WSS) if \begin{align}\mathbf{E}[X_{t}]&=\text{constant}\\\mathbf{E}[X_{t_{1}}X_{t_{2}}]&=\text{depends only on }|t_{1}-t_{2}|\end{align}

#### Flashcard 7609096998156

Question

The process $$X_{t}$$ is said to be wide sense stationary (WSS) if [...]

\begin{align}\mathbf{E}[X_{t}]&=\text{constant}\\\mathbf{E}[X_{t_{1}}X_{t_{2}}]&=\text{depends only on }|t_{1}-t_{2}|\end{align}

status measured difficulty not learned 37% [default] 0

The process $$X_{t}$$ is said to be wide sense stationary (WSS) if \begin{align}\mathbf{E}[X_{t}]&=\text{constant}\\\mathbf{E}[X_{t_{1}}X_{t_{2}}]&=\text{depends only on }|t_{1}-t_{2}|\end{align}

#### Annotation 7609098571020

 稳态信号或广义稳态信号的自相关函数定义 For a stationary or WSS process, the autocorrelation function is defined as $$r_{XX}(\tau)=\mathbf{E}[X_{t}X_{t+\tau}]$$

#### Flashcard 7609099881740

Question
For a stationary or WSS process, the autocorrelation function is defined as [...]
$$r_{XX}(\tau)=\mathbf{E}[X_{t}X_{t+\tau}]$$

status measured difficulty not learned 37% [default] 0

For a stationary or WSS process, the autocorrelation function is defined as $$r_{XX}(\tau)=\mathbf{E}[X_{t}X_{t+\tau}]$$

#### Annotation 7609107221772

 伯努利分布的定义 伯努利分布的定义：$$\mu[p]=p \delta_0+(1-p) \delta_1$$

#### Flashcard 7609109056780

Question

$$\mu[p]=p \delta_0+(1-p) \delta_1$$

status measured difficulty not learned 37% [default] 0

#### Annotation 7609110629644

 伯努利分布的期望 伯努利分布的期望：$$\mathrm{E}[X] =p$$

#### Annotation 7609114037516

 伯努利分布的方差 伯努利分布的方差：$$\operatorname{Var}[X] =p(1-p)$$

#### Annotation 7609117445388

 二项分布的定义 二项分布的定义：$$\displaystyle\mu[p]=\sum_{k=0}^n\left(\begin{array}{l}n \\k\end{array}\right) p^k(1-p)^{n-k} \delta_k$$

#### Annotation 7609124261132

 二项分布的期望 二项分布的期望：$$\mathrm{E}[X] =np$$
 二项分布的方差 二项分布的方差：$$\operatorname{Var}[X] =np(1-p)$$