Pardon my ignorance

but can someone provide explanation for these 'why'?

Amit Goyal wrote

Some of you have written to me asking what they ask in an ISI interview. Here is my reply:

ISI interview will be not too different from solving problems in an economics entrance exam. Its just that you will now be asked to solve those problems on the board. To prepare for it you need to practice problem solving. Unlike entrance exams, there is lesser or no scope to skip explanations that goes with each step. For example: Suppose you are asked to solve the following problem:

Let X and Y be i.i.d Uniform [0, 1]. Find the cumulative distribution function of Z = max{X, Y}.

Lets say you know how to do it and you wrote:

For 0 < z < 1,

Pr(Z ≤ z)

= Pr(max{X, Y} ≤ z)

= Pr(X ≤ z, Y ≤ z) (why?)

= Pr(X ≤ z)Pr(Y ≤ z) (why?)

= z^2

Remember to answer those whys along with the derivation.