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Consider three independent random variables $A$, $B$ and $C$ and a fixed number $K$. Can we rewrite the $textPr left(A geq K cap A geq max left(B,C right) right)$ as $textPr left(A geq K cap A geq B right) textPr left(B >C right)$+$textPr left(A geq K cap A geq C right) textPr left(B leq C right)$?

probability probability-theory stochastic-processes stochastic-calculus

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asked yesterday

miladmilad

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$begingroup$

Consider three independent random variables $A$, $B$ and $C$ and a fixed number $K$. Can we rewrite the $textPr left(A geq K cap A geq max left(B,C right) right)$ as $textPr left(A geq K cap A geq B right) textPr left(B >C right)$+$textPr left(A geq K cap A geq C right) textPr left(B leq C right)$?

probability probability-theory stochastic-processes stochastic-calculus

share|cite|improve this question

asked yesterday

miladmilad

11

$endgroup$

add a comment | 

$begingroup$

Consider three independent random variables $A$, $B$ and $C$ and a fixed number $K$. Can we rewrite the $textPr left(A geq K cap A geq max left(B,C right) right)$ as $textPr left(A geq K cap A geq B right) textPr left(B >C right)$+$textPr left(A geq K cap A geq C right) textPr left(B leq C right)$?

probability probability-theory stochastic-processes stochastic-calculus

share|cite|improve this question

asked yesterday

miladmilad

11

$endgroup$

share|cite|improve this question

asked yesterday

miladmilad

11

share|cite|improve this question

asked yesterday

miladmilad

11

asked yesterday

miladmilad

11

asked yesterday

miladmilad

11