random_soldier1337

How does one formulate continuous probabilities/pdfs?

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Discrete examples are easy enough. Toss a coin, 1/2, toss a die, 1/6.

Continuous examples, Probability of a nucleus decaying during observation, 1-exp(-λt), Probability of a neutron moves x without interaction, exp(-Σx), where Σ can be assumed to be the inverse of the mean free path i.e. the distance a neutron travels without interaction on average.

My point is that I don't really have an idea as to how these continuous probabilities are derived. Any assistance?

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Posted (edited)
15 minutes ago, random_soldier1337 said:

My point is that I don't really have an idea as to how these continuous probabilities are derived. Any assistance?

What does the probability tell you?

Why is the probability of getting heads in a coin flip one half and what does that mean?

Once you have this clear you can move on to probabilities of continuous distributions.

Edited by studiot

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Posted (edited)

Well in the case of the coin it tells me that there are 2 random events that can happen when I flip a coin. The chance that one or the other takes place is 1/2 under the assumption both sides are affected by the same unbiased factors.

Now, taking for example the probability of a nucleus decaying, I know that the number of nuclei in a sample N = Noexp(-λt), where No is the initial amount. Looking at the probability of a nucleus decaying another way, I could put it as 1-N/No. I'm not really sure I understand. 1- the percentage of nuclei remaining at a given time gives me the probability?

EDIT: Or do you mean to say that they are derived by observation and large sample sizes of a phenomenon?

Edited by random_soldier1337

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