A game provides two options of choosing a number:

A game provides two options of choosing a number: 1) randomly generate a real number in the range [0,1], denoted as X, andtake its second power; 2) randomly generate two real numbers in the range [0,1], independently, denoted as Y and Z, and take theirproduct. Your goal is to decide which option gives a larger value more often.

1. Calculate the PDF of the result given by option 1, i.e., the PDF of X2.2. Calculate the PDF of the result given by option

2, i.e., the PDF of Y Z.3. Calculate the probability that option 2 gives a larger value, i.e., P(Y Z > X2), and point out which option is better