Financial Risk Manager Part 1

Explanation

A continuous random variable is a variable that can take on any value within a given range or interval, including fractional values. In contrast, a discrete random variable can only take on specific, countable values (usually integers).

Let's analyze each item:

I. Stock indices - ✅ Continuous Stock indices can take on any value (e.g., S&P 500 at 2433.45, 2433.67, etc.). Between any two values, there are infinite possible values.

II. The weight of 20 FRM candidates - ✅ Continuous Weight measurements can take on any value within a range (e.g., 150.5 lbs, 150.52 lbs, 150.523 lbs, etc.). Weight is a continuous measurement.

III. Biannual share dividends received over a 10-year period - ✅ Continuous Dividend amounts can be any value (e.g., $2.35, $2.357, etc.). Money amounts are continuous variables.

IV. The number of holidays in a given year - ❌ Discrete The number of holidays must be a whole number (e.g., 10, 11, 12 holidays). You cannot have 10.5 holidays.

V. The annual number of FRM exam candidates in the last 10 years - ❌ Discrete The number of candidates must be a whole number (e.g., 5,000 candidates, not 5,000.5 candidates).

Therefore, only items I, II, and III are continuous random variables, which corresponds to option B.

Key Concept: Continuous variables can take on any value within an interval (including decimals/fractions), while discrete variables can only take on specific, countable values (typically integers).