Financial Risk Manager Part 1

Statement B is false but its converse is true: The normal distribution has skewness = 0 and kurtosis = 3. In fact, the kurtosis of other distributions is measured relative to 3, which is the kurtosis of the normal distribution.

Detailed Explanation:

1. Option A is TRUE - The normal distribution is completely characterized by its mean (μ) and variance (σ²). These two parameters determine the entire shape and location of the distribution.

2. Option B is FALSE - This is the correct answer. The normal distribution has:

   • Skewness = 0 (perfectly symmetric)
   • Kurtosis = 3 (mesokurtic)

   The statement incorrectly reverses these values. The kurtosis of 3 is often used as a reference point, with distributions having kurtosis > 3 called leptokurtic (fat-tailed) and those with kurtosis < 3 called platykurtic (thin-tailed).

3. Option C is TRUE - A fundamental property of normal distributions is that any linear combination of normally distributed random variables is also normally distributed. This property makes the normal distribution particularly useful in finance and statistics.

4. Option D is TRUE - The normal distribution has infinite tails, meaning extreme events are possible (though increasingly improbable). The probability density function approaches zero asymptotically but never actually reaches zero, allowing for theoretically infinite values.