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This question involves finding the statistical properties of a discrete-time random process \( X[n] = e^{-An} \), where \( n \geq 1 \) and \( A \) is a standard normal random variable (i.e., \( A \sim N(0,1) \)).

### Let's go through each requirement:
1. **Expectation Function** \( E[X[n]] \):
   To find the expectation of \( X[n] \), we calculate \( E[e^{-An}] \). Since \( A \) is a normal random variable with mean \( 0 \) and variance \( 1 \), we use the moment-generating function of a normal distribution:
   \[
   E[e^{-An}] = e^{\frac{n^2}{2}}.
   \]
   
2. **Mean Function** \( E[X[n]] \):
   The mean function is the same as the expectation function found above, so:
   \[
   \text{Mean Function } = E[X[n]] = e^{\frac{n^2}{2}}.
   \]

3. **Variance Function** \( \text{Var}(X[n]) \):
   To find the variance, we use:
   \[
   \text{Var}(X[n]) = E[X[n]^2] - (E[X[n]])^2.
   \]
   We calculate \( E[X[n]^2] = E[e^{-2An}] = e^{2n^2} \), and thus:
   \[
   \text{Variance} = e^{2n^2} - (e^{n^2})^2 = e^{2n^2} - e^{2n^2} = 0.
   \]

4. **Autocorrelation Function** \( R_X(n,m) = E[X[n]X[m]] \):
   The

离散时间随机过程具有通想表达: X[n] = e^{-An}, n >= 1, A 是标准正态一维随机变量，试求 X[n] 的均值函数、均方函数、方差函数、以及自相关函数。

Explore the statistical properties of the discrete-time random process X[n] = e^{-An}, where A is a standard normal random variable. This includes finding the mean function, variance function, and autocorrelation function. Suitable for undergraduate students studying probability and random processes.

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