Question

If \(X \sim N(\mu, \sigma^2)\). The maximum ordinate is at \(X = \mu\) and is given by:

• A. \(\sigma \sqrt{2\pi}\)
• B. \(\frac{1}{\sigma \sqrt{2\pi}}\)
• C. \(\sigma \sqrt{2\pi} e\)
• D. \(\frac{1}{\sigma \sqrt{2\pi e}}\)

Hint:

The peak value of any probability density function is its maximum ordinate.
For a standard normal distribution (\(\mu=0, \sigma=1\)), this peak value simplifies directly to \(\frac{1}{\sqrt{2\pi}} \approx 0.3989\).

Answer 1

The Correct Option is B