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The question you have shared involves finding the mode of a normally distributed random variable \( X \). Here's the question in LaTeX form:

```latex
If the random variable \( X \sim \mathcal{N}(\mu, \sigma^2) \), then what is the mode of \( X \)?
```

Would you like me to explain how to find the mode of a normal distribution? 

Here are some related questions for further exploration:

1. What is the probability density function (PDF) of a normal distribution?
2. What are the key characteristics of a normal distribution (mean, median, mode)?
3. How does variance (\( \sigma^2 \)) affect the shape of a normal distribution?
4. What is the relationship between the mean, median, and mode in a normal distribution?
5. How do you calculate probabilities using the cumulative distribution function (CDF) for a normal distribution?

**Tip**: In a normal distribution \( \mathcal{N}(\mu, \sigma^2) \), the mode is always equal to the mean \( \mu \), as it is the peak of the bell curve.

If the random variable X ~ N(μ, σ^2), then what is the mode of X?

Learn how to find the mode of a normally distributed random variable X ~ N(μ, σ^2). This problem covers key statistical concepts of normal distribution, including the formula and the fact that the mode is equal to the mean μ in such a distribution.

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