121
Off Topic / Statistics Question
« on: May 28, 2005, 03:00:17 PM »
Here's my try on the problem.
If B, C, D, E are independent and A=(B||C||D||E), then ~A=~B&~C&~D&~E (note: '~A' means 'not A') and P(A)=1-(1-P(B))(1-P( C))(1-P(D))(1-P(E)). To change P(A) and conserve the relative probabilities of B, C, D, E, you need to solve a quartic equation.
But I think it would be simpler to define a as the expectation value of the number of events. In that case a = P(B)+P( C)+P(D)+P(E) and it's straightforward to rescale the probabilities.
If B, C, D, E are independent and A=(B||C||D||E), then ~A=~B&~C&~D&~E (note: '~A' means 'not A') and P(A)=1-(1-P(B))(1-P( C))(1-P(D))(1-P(E)). To change P(A) and conserve the relative probabilities of B, C, D, E, you need to solve a quartic equation.
But I think it would be simpler to define a as the expectation value of the number of events. In that case a = P(B)+P( C)+P(D)+P(E) and it's straightforward to rescale the probabilities.