How to write this probability in a paper?

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I would like to know how to write the following probability in a scientific way:

$S=P(x_{1}<y, x_{2}<y,..., x_{n}<y, x_{1}>0, x_{2}>0,..., x_{n}>0)$

Can I use matrix notation for proper representing these multiple conditions such that:

$S=P(X<y, X>0)$

where $ X=[x_{1},x_{2},...,x_{n}]$