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- Thread starter oneamp
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mathman

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No. Two events can occur at the same time only if they have discrete distributions. When both have continuous distributions (and are independent) the probability of happening at the same time is 0.

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Yes true :) How can I calculate the probability that between some points 'a' and 'b' in time, two events with these PDFs will occur? For example, if one PDF describes the probability that a light will be orange, and another PDF describes probability for a green light, and I want to know the chances that there will be an orange and a green light illuminated "at the same time" between times 'a' and 'b'?

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Office_Shredder

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Thank you very much

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That's not true at all. Suppose ##X## and ##Y## are independent normally distributed random variables. Let ##A## be the event that ##X > 0## and ##B## be the event that ##Y > 0##. Clearly the probability of ##A \cap B## is nonzero.No. Two events can occur at the same time only if they have discrete distributions. When both have continuous distributions (and are independent) the probability of happening at the same time is 0.

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mathman

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That's not true at all. Suppose ##X## and ##Y## are independent normally distributed random variables. Let ##A## be the event that ##X > 0## and ##B## be the event that ##Y > 0##. Clearly the probability of ##A \cap B## is nonzero.

You misunderstood the point of the original question. He was asking about something like the probability that X=Y when both have continuous distributions.

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