確かに、対称確率分布を使うことの弱点を示すPythonの例をいくつか紹介しよう：

1.柔軟性の欠如：
対称確率分布の柔軟性の欠如を示すために、scipy.statsライブラリを使って正規分布と二峰性分布を比較することができます：

```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

# Generate a bimodal distribution
x = np.concatenate((np.random.normal(-2, 1, 1000), np.random.normal(2, 1, 1000)))

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins=30, density=True, alpha=0.5)
xmin, xmax = plt.xlim()
x_range = np.linspace(xmin, xmax, 100)
p = norm.pdf(x_range, mu, std)
plt.plot(x_range, p, 'k', linewidth=2)
plt.show()
```

結果のプロットは、正規分布が二峰性のデータにあまり適合しないことを示しています：

2.歪度：
歪度の問題を実証するために、歪んだデータセットを生成し、scipy.statsライブラリを使って正規分布と歪んだ分布を比較することができます：

```python
from scipy.stats import skewnorm

# Generate a skewed distribution
x = skewnorm.rvs(5, size=1000)

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins=30, density=True, alpha=0.5)
xmin, xmax = plt.xlim()
x_range = np.linspace(xmin, xmax, 100)
p = norm.pdf(x_range, mu, std)
plt.plot(x_range, p, 'k', linewidth=2)
plt.show()
```

結果のプロットは、正規分布が歪んだデータにあまりフィットしないことを示しています：

3.外れ値
外れ値：対称確率分布の外れ値に対する感度を示すために，データセットに外れ値を加え，scipy.statsライブラリを使って正規分布と元の分布を比較することができる：

```python
# Generate a normal distribution
x = np.random.normal(0, 1, 1000)

# Add some outliers
x = np.concatenate((x, [10, -10]))

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins=30, density=True, alpha=0.5)
xmin, xmax = plt.xlim()
x_range = np.linspace(xmin, xmax, 100)
p = norm.pdf(x_range, mu, std)
plt.plot(x_range, p, 'k', linewidth=2)
plt.show()
```

結果のプロットは、正規分布が外れ値をあまりうまく捉えていないことを示しています：

4.限られた記述力：
対称確率分布の記述力に限界があることを示すために，scipy.statsライブラリを用いて，マルチモーダルデータセットを生成し，正規分布と実際のデータを比較することができる：

```python
# Generate a multimodal distribution
x = np.concatenate((np.random.normal(-2, 1, 500), np.random.normal(2, 1, 500), np.random.normal(5, 1, 500)))

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins)
```
Certainly, here are some Python examples to demonstrate the weaknesses of using a symmetric probability distribution:

1. Lack of flexibility:
To demonstrate the lack of flexibility of symmetric probability distributions, we can compare the normal distribution to a bimodal distribution using the scipy.stats library:

```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

# Generate a bimodal distribution
x = np.concatenate((np.random.normal(-2, 1, 1000), np.random.normal(2, 1, 1000)))

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins=30, density=True, alpha=0.5)
xmin, xmax = plt.xlim()
x_range = np.linspace(xmin, xmax, 100)
p = norm.pdf(x_range, mu, std)
plt.plot(x_range, p, 'k', linewidth=2)
plt.show()
```

The resulting plot shows that the normal distribution does not fit the bimodal data very well:

2. Skewness:
To demonstrate the issue of skewness, we can generate a skewed dataset and compare the normal distribution to the skewed distribution using the scipy.stats library:

```python
from scipy.stats import skewnorm

# Generate a skewed distribution
x = skewnorm.rvs(5, size=1000)

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins=30, density=True, alpha=0.5)
xmin, xmax = plt.xlim()
x_range = np.linspace(xmin, xmax, 100)
p = norm.pdf(x_range, mu, std)
plt.plot(x_range, p, 'k', linewidth=2)
plt.show()
```

The resulting plot shows that the normal distribution does not fit the skewed data very well:

3. Outliers:
To demonstrate the sensitivity of symmetric probability distributions to outliers, we can add some outliers to a dataset and compare the normal distribution to the original distribution using the scipy.stats library:

```python
# Generate a normal distribution
x = np.random.normal(0, 1, 1000)

# Add some outliers
x = np.concatenate((x, [10, -10]))

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins=30, density=True, alpha=0.5)
xmin, xmax = plt.xlim()
x_range = np.linspace(xmin, xmax, 100)
p = norm.pdf(x_range, mu, std)
plt.plot(x_range, p, 'k', linewidth=2)
plt.show()
```

The resulting plot shows that the normal distribution does not capture the outliers very well:

4. Limited descriptive power:
To demonstrate the limited descriptive power of symmetric probability distributions, we can generate a multimodal dataset and compare the normal distribution to the actual data using the scipy.stats library:

```python
# Generate a multimodal distribution
x = np.concatenate((np.random.normal(-2, 1, 500), np.random.normal(2, 1, 500), np.random.normal(5, 1, 500)))

# Fit a normal distribution to the data
mu, std = norm.fit(x)

# Plot the histogram and the fitted normal distribution
plt.hist(x, bins)
```