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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

Compared with the standard normal distribution, which statement about a Student's t distribution with 5 degrees of freedom is correct?

A t distribution with 5 degrees of freedom has fatter tails than the standard normal and a variance of k/(k-2) = 5/3, which is greater than 1. It is symmetric, not skewed, and converges to the normal as degrees of freedom increase.

  1. AIt has thinner tails and a lower variance than the standard normal
  2. BIt has fatter tails, and its variance is 5/3, exceeding 1Correct
  3. CIt is skewed to the right, like the chi-squared distribution
  4. DIt has fatter tails, and its variance is 5/7

Explanation

The t distribution is symmetric with excess kurtosis and fatter tails than the normal. Its variance is k/(k-2) = 5/3 ≈ 1.67 for k > 2, which exceeds 1 and approaches 1 as k grows. Skewness applies to chi-squared, not t, and 5/7 is a wrong formula.

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