Which Variable Is Largest

Ties have probability zero for continuous random variables.

By symmetry, each of the three variables is equally likely to be the maximum.

1. 1. Use symmetry

   Since X, Y and Z are exchangeable and continuous, each variable is equally likely to attain the maximum value.

   $$P(X=\max )=P(Y=\max )=P(Z=\max )$$

2. 2. Normalize

   The three probabilities sum to $1$.

   $$P(X=\max )=\frac{1}{3}$$

Answer: 1/3