Question

The square of a standard normal variate is a
1. Beta distribution
2. Cauchy distribution
3. Chi-square distribution
4. F-distribution

Answer 1

Correct Answer - Option 3 : Chi-square distribution

Concept:

The standard normal random variable U is a normally distributed variable with mean zero and variance one, i.e. U ∼ N (0, 1).

The chi-square distribution is the distribution of the sum of squared standard normal variates.

Now consider a random variable Z = U². The distribution of the random variable Z is an example of the chi-square distribution. Z ∼ χ²