Explanation

Let's analyze each option:

Option A: "is skewed to the left."

• This is FALSE. A lognormal distribution is skewed to the RIGHT, not to the left. The lognormal distribution has positive skewness because the exponential function transforms the symmetric normal distribution into one with a long right tail.

Option B: "is often used to model stock prices."

• This is TRUE. The lognormal distribution is commonly used to model stock prices in finance because:
  1. Stock prices cannot be negative (lognormal distribution has positive values only)
  2. Returns are often assumed to be normally distributed, and if returns are normally distributed, then stock prices are lognormally distributed
  3. It captures the positive skewness often observed in financial asset prices

Option C: "has a mean equal to exp(μ), where μ is the mean of X."

• This is FALSE. The mean of a lognormal distribution Y = exp(X), where X ~ N(μ, σ²), is: $E[Y] = \exp\left(\mu + \frac{\sigma^2}{2}\right)$

  Not simply exp(μ). The correct formula includes the variance term σ²/2. The median of the lognormal distribution is exp(μ), but the mean is larger due to the positive skewness.

Correct Answer: B is correct, and C is incorrect.

Key Points:

• Lognormal distribution: Y = exp(X) where X ~ N(μ, σ²)
• Mean: E[Y] = exp(μ + σ²/2)
• Median: exp(μ)
• Variance: Var(Y) = [exp(σ²) - 1] × exp(2μ + σ²)
• Always positive values
• Right-skewed (positive skewness)
• Widely used in finance for modeling stock prices, option pricing (Black-Scholes model), and other financial variables that cannot be negative.